Two Dimensional Maps
January 18 - April 28, 2023
Important developments in one-dimensional real dynamics include substantial progress in our understanding of circle maps, quadratic maps of the interval, polynomial maps of an interval, unimodal and multimodal maps. Some of the highlights are the work by Herman and Yoccoz on circle maps, Swiatek-Graczyk and Lyubich on density of hyperbolicity for quadratic maps, Lyubich’s work on stochasticity versus periodicity, as well as work by de Melo, van Strien, Shen, Avila and others. The area has been extremely successful but less progress has been made in higher dimension. The present program is mainly emphasizing the theory of two- dimensional maps where there are many open problems, but we may also consider dimension ≥ 3 and even infinite dimension (PDE:s). The subjects investigated include area preserving maps, dissipative maps, Anosov systems, quasi periodic skew products, hyperbolic skew products, maps of entropy zero, and piecewise isometries.
During the research program, there will be two workshops:
- Workshop I: March 13 – 17, 2023
- Workshop II: April 11 – 15, 2023
Seminars Scroll to the next upcoming seminar
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Raul Ures: Partial hyperbolicity in dimension 3: the ergodicity conjecture January 19 14:00 - 15:00 -
Jana Rodriguez Herz: Unique SRB measure maximizing entropy for a family of non-conservative diffeomorphisms January 19 15:00 - 16:00 Jana Rodriguez Herz: Unique SRB measure maximizing entropy for a family of non-conservative diffeomorphisms
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Federico Rodrigues-Herz: Rigidity for Anosov in low dimensions January 24 14:00 - 14:45 Federico Rodrigues-Herz: Rigidity for Anosov in low dimensions
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Federico Rodrigues-Herz: Rigidity for Anosov in low dimensions (cont.) January 24 15:00 - 15:45 Federico Rodrigues-Herz: Rigidity for Anosov in low dimensions (cont.)
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Reza Mohammadpour: SRB measures for partially hyperbolic systems January 26 14:00 - 15:00 Reza Mohammadpour: SRB measures for partially hyperbolic systems
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Magnus Aspenberg: Perturbations of slowly recurrent Collet-Eckmann maps January 26 15:00 - 16:00 Magnus Aspenberg: Perturbations of slowly recurrent Collet-Eckmann maps
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Raluca Tanase: On the dynamics of the complex Hénon map I January 31 14:00 - 15:00 Raluca Tanase: On the dynamics of the complex Hénon map I
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Mats Bylund: Critical recurrence in the real quadratic family January 31 15:00 - 16:00 Mats Bylund: Critical recurrence in the real quadratic family
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Remus Rado: On the dynamics of the complex Hénon map II February 02 14:00 - 15:00 Remus Rado: On the dynamics of the complex Hénon map II
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Weiwei Cui: Speiser meets Misiurewicz February 02 15:00 - 16:00 Weiwei Cui: Speiser meets Misiurewicz
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Boris Petkovic: KAM method in non-abelian setting February 09 14:00 - 15:00 Boris Petkovic: KAM method in non-abelian setting
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Kevin Smith: Almost-periodicity of zeta functions February 09 15:00 - 16:00 Kevin Smith: Almost-periodicity of zeta functions
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Jonguk Yang: A priori bounds for unimodal diffeomorphisms in dimension two February 14 14:00 - 16:00 Jonguk Yang: A priori bounds for unimodal diffeomorphisms in dimension two
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David Marti-Pete: Wandering domains in transcendental dynamics: topology and dynamics February 16 14:00 - 15:00 David Marti-Pete: Wandering domains in transcendental dynamics: topology and dynamics
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Carlangelo Liverani: CLT with error terms for sequential Dynamical systems February 16 15:00 - 16:00 Carlangelo Liverani: CLT with error terms for sequential Dynamical systems
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Michael Rams: Cocycles of circle diffeomorphisms February 21 14:00 - 16:00 Michael Rams: Cocycles of circle diffeomorphisms
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Noah Cockram: Renormalizability of Translated Cone Exchanges February 23 14:00 - 15:00 Noah Cockram: Renormalizability of Translated Cone Exchanges
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Sven Sandfeldt: Centralizer rigidity for partially hyperbolic toral automorphisms February 23 15:00 - 16:00 Sven Sandfeldt: Centralizer rigidity for partially hyperbolic toral automorphisms
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A. Öberg: Continuous eigenfunctions of the transfer operator, and uniqueness and mixing properties of Doeblin measures March 02 14:00 - 15:00 A. Öberg: Continuous eigenfunctions of the transfer operator, and uniqueness and mixing properties of Doeblin measures
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Raphael Krikorian: On local integrability of real analytic conservative diffeomorphisms in dimension 2 March 02 15:00 - 16:00 Raphael Krikorian: On local integrability of real analytic conservative diffeomorphisms in dimension 2
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Raphael Krikorian: On local integrability of real analytic conservative diffeomorphisms in dimension 2, II March 07 14:00 - 15:00 Raphael Krikorian: On local integrability of real analytic conservative diffeomorphisms in dimension 2, II
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Alexander Bufetov: The spectral co-cycle for translation flows March 07 15:00 - 16:00 Alexander Bufetov: The spectral co-cycle for translation flows
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Workshop: Criteria for recurrence and transience for random walks with general internal states, Davit Karagulyan March 13 10:15 - 11:15 Workshop: Criteria for recurrence and transience for random walks with general internal states, Davit Karagulyan
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Workshop: Monotone families of circle diffeomorphisms driven by expanding circle maps, Kristian Bjerklöv March 13 11:30 - 12:30 Workshop: Monotone families of circle diffeomorphisms driven by expanding circle maps, Kristian Bjerklöv
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Workshop: The Real Teapot, Michal Misiurewicz March 13 14:00 - 15:00 Workshop: The Real Teapot, Michal Misiurewicz
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Workshop: The critical locus of a Hénon map, Remus Radu March 14 10:15 - 11:15 Workshop: The critical locus of a Hénon map, Remus Radu
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Workshop: A dichotomy for commuting parabolic linear maps on the torus, Danijela Damjanovic March 14 11:30 - 12:30 Workshop: A dichotomy for commuting parabolic linear maps on the torus, Danijela Damjanovic
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Workshop: A parameter almost sure invariance principle for the quadratic, Tomas Persson family March 14 14:00 - 15:00 Workshop: A parameter almost sure invariance principle for the quadratic, Tomas Persson family
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Workshop: Nontrivial embeddings of interval exchange transformations into piecewise isometries (Online), Pedro Peres March 15 10:15 - 11:15 Workshop: Nontrivial embeddings of interval exchange transformations into piecewise isometries (Online), Pedro Peres
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Workshop: Planar piecewise isometries: some examples and open problems, Peter Ashwin March 15 11:30 - 12:30 Workshop: Planar piecewise isometries: some examples and open problems, Peter Ashwin
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Workshop: Renormalizability of Translated Cone Exchanges, Noah Cockram March 15 12:30 - 13:30 Workshop: Renormalizability of Translated Cone Exchanges, Noah Cockram
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Workshop: Proof of A Priori Bounds for Unimodal Diffeomorphisms in Dimension Two, Jonguk Yang March 16 10:15 - 11:15 Workshop: Proof of A Priori Bounds for Unimodal Diffeomorphisms in Dimension Two, Jonguk Yang
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Workshop: 2D-Sinai billiards maps and flows via transfer operators, Viviane Baladi March 16 11:30 - 12:30 Workshop: 2D-Sinai billiards maps and flows via transfer operators, Viviane Baladi
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Workshop: Thermodynamics of potentials with logarithmic singularities, Jörg Schmeling March 16 14:00 - 15:00 Workshop: Thermodynamics of potentials with logarithmic singularities, Jörg Schmeling
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Discussion session March 17 10:15 - 11:15 Discussion session
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Peter Ashwin: Relating measure and statistical notions of non-autonomous attraction March 21 14:00 - 15:00 Peter Ashwin: Relating measure and statistical notions of non-autonomous attraction
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Michal Misiurewicz: Topological entropy of generalized Bunimovich stadium billiards March 21 15:00 - 16:00 Michal Misiurewicz: Topological entropy of generalized Bunimovich stadium billiards
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Sandro Vaienti: Thermodynamic formalism of random open systems March 23 14:00 - 15:00 Sandro Vaienti: Thermodynamic formalism of random open systems
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Jacopo de Simoi: Length spectrum determination of billiards March 23 15:00 - 16:00 Jacopo de Simoi: Length spectrum determination of billiards
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Tere M-Seara: Chaotic dynamics and oscillatory motions in the three body problem March 28 14:00 - 15:00 Tere M-Seara: Chaotic dynamics and oscillatory motions in the three body problem
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Sandro Vaienti: Perturbation of unimodal maps with application to synchronisation March 28 15:00 - 16:00 Sandro Vaienti: Perturbation of unimodal maps with application to synchronisation
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Maria Saprykina: Nonconmutative coboundary equations over integrable systems March 29 11:00 - 12:00 Maria Saprykina: Nonconmutative coboundary equations over integrable systems
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Arek Goetz: Global and local behavior of orbits in the two halfplane map. Computer aided renormalization techniques. March 30 14:00 - 15:00 Arek Goetz: Global and local behavior of orbits in the two halfplane map. Computer aided renormalization techniques.
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Jacopo de Simoi: Length spectrum determination of billiards II March 30 15:00 - 16:00 Jacopo de Simoi: Length spectrum determination of billiards II
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Paulo Varandas: Thermodynamic formalism for expanding measures April 04 14:00 - 15:00 Paulo Varandas: Thermodynamic formalism for expanding measures
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Warwick Tucker: Relative equilibria for the n-body problem April 04 15:00 - 16:00 Warwick Tucker: Relative equilibria for the n-body problem
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Workshop: Marked Length Spectral determination of analytic chaotic billiards April 11 09:30 - 10:30 Workshop: Marked Length Spectral determination of analytic chaotic billiards
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Workshop: Ergodicity of skew-products over IETs April 11 11:00 - 12:00 Workshop: Ergodicity of skew-products over IETs
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Workshop: A dynamical system model of systemic risk in finance April 11 13:30 - 14:30 Workshop: A dynamical system model of systemic risk in finance
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Workshop: Newhouse phenomenon in the complex Hénon family April 11 15:00 - 16:00 Workshop: Newhouse phenomenon in the complex Hénon family
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Workshop: Typical rotation number for families of circle maps with singularities April 12 09:30 - 10:30 Workshop: Typical rotation number for families of circle maps with singularities
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Workshop: On regularity of conjugacies of generalized IETs April 12 11:00 - 12:00 Workshop: On regularity of conjugacies of generalized IETs
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Workshop: Positivity and Continuity of the Lyapunov Exponents of 2d cocycles April 12 13:30 - 14:30 Workshop: Positivity and Continuity of the Lyapunov Exponents of 2d cocycles
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Workshop: The Calabi invariant of an irrational pseudo rotation; a finite dimensional approach April 12 15:00 - 16:00 Workshop: The Calabi invariant of an irrational pseudo rotation; a finite dimensional approach
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Workshop: Omega Functions April 13 09:30 - 10:30 Workshop: Omega Functions
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Workshop: On Takens-Yoccoz’ theorem in finite regularity April 13 11:00 - 12:00 Workshop: On Takens-Yoccoz’ theorem in finite regularity
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Workshop: Deformations of Z^2-actions in dimension 1 April 14 09:30 - 10:30 Workshop: Deformations of Z^2-actions in dimension 1
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Workshop: Stability of the Lyapunov exponents under random noise April 14 11:00 - 12:00 Workshop: Stability of the Lyapunov exponents under random noise
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Workshop: Structure of Feigenbaum Henon maps April 14 13:30 - 14:30 Workshop: Structure of Feigenbaum Henon maps
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Workshop: 4-winged Lorenz attractor in the 3-dimensional Henon map April 14 15:00 - 16:00 Workshop: 4-winged Lorenz attractor in the 3-dimensional Henon map
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Workshop: Furstenberg Theorem and its generalizations April 15 09:30 - 10:30 Workshop: Furstenberg Theorem and its generalizations
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Workshop: The dynamics of conformally Hamiltonian flows: dissipativity and conservativity April 15 11:00 - 12:00 Workshop: The dynamics of conformally Hamiltonian flows: dissipativity and conservativity
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Enrique Pujals: Mildly dissipative maps of the disk with zero entropy I April 18 14:20 - 15:00 Enrique Pujals: Mildly dissipative maps of the disk with zero entropy I
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Enrique Pujals: Mildly dissipative maps of the disk with zero entropy II April 18 15:00 - 16:00 Enrique Pujals: Mildly dissipative maps of the disk with zero entropy II
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Sylvain Crovisier: Mildly dissipative maps of the disk with zero entropy III April 20 14:00 - 15:00 Sylvain Crovisier: Mildly dissipative maps of the disk with zero entropy III
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Sylvain Crovisier: Mildly dissipative maps of the disk with zero entropy IV April 20 15:00 - 16:00 Sylvain Crovisier: Mildly dissipative maps of the disk with zero entropy IV
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Sébastien Biebler: Blenders and almost blenders April 25 14:00 - 15:00 Sébastien Biebler: Blenders and almost blenders
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Pierre Berger: Analytic pseudo-rotations April 25 15:00 - 16:00 Pierre Berger: Analytic pseudo-rotations
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Anton Gorodetski: Dynamical Methods in Spectral Theory of Ergodic Schrodinger Operators April 27 13:00 - 14:00 Anton Gorodetski: Dynamical Methods in Spectral Theory of Ergodic Schrodinger Operators
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Pablo Gutiérrez Barrientos: Minimal Strong Foliations in Skew-products of Iterated Function Systems April 27 14:00 - 15:00 Pablo Gutiérrez Barrientos: Minimal Strong Foliations in Skew-products of Iterated Function Systems
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Jacek Graczyk: Mandelbrot set viewed from smooth traversing curves April 27 15:00 - 16:00 Jacek Graczyk: Mandelbrot set viewed from smooth traversing curves
Recordings
Participants
| Name | University | Country | Arrival and Departure |
|---|---|---|---|
| Demi Allen | University: University of Exeter | Country: United Kingdom | Arrival and Departure: |
| Marie-Claude Arnaud | University: IMJ-PRG, University Paris-Cité | Country: France | Arrival and Departure: Apr 14 - Apr 29 |
| Peter Ashwin | University: University of Exeter | Country: United Kingdom | Arrival and Departure: Mar 14 - Apr 8 |
| Magnus Aspenberg | University: Lund University | Country: Sweden | Arrival and Departure: Jan 23, Feb 28. Apr 18 - Jan 27, Mar 10, Apr 22 |
| Viviane Baladi | University: CNRS | Country: France | Arrival and Departure: Mar 6 - Mar 17 |
| Michael Benedicks (Organizer) | University: KTH Royal Institute of Technology | Country: Sweden | Arrival and Departure: Jan 18 - Apr 28 |
| Pierre Berger | University: Institute of Mathematics of Jussieu | Country: France | Arrival and Departure: Apr 25 - Apr 27 |
| Sebastien Biebler | University: University Paris-Cité | Country: France | Arrival and Departure: Apr 22 - Apr 29 |
| Kristian Bjerklöv | University: KTH Royal Institute of Technology | Country: Sweden | Arrival and Departure: Jan 18 - Apr 28 |
| Alexander Bufetov (Online) | University: CNRS | Country: France | Arrival and Departure: |
| Mats Bylund | University: Lund University | Country: Sweden | Arrival and Departure: Jan 18 - Apr 28 |
| Noah Cockram | University: University of Exeter | Country: United Kingdom | Arrival and Departure: Jan 18 - Apr 18 |
| Sylvain Crovisier | University: CNRS | Country: France | Arrival and Departure: Apr 17 - Apr 21 |
| Weiwei Cui | University: Lund University | Country: Sweden | Arrival and Departure: Jan 22 - Apr 28 |
| Danijela Damjanovic | University: KTH Royal Institute of Technology | Country: Sweden | Arrival and Departure: Jan 24 - Apr 28 |
| Dmitry Dolgopyat (Online) | University: University of Maryland | Country: United States | Arrival and Departure: |
| Kostiantyn Drach | University: Institute of Science and Technology Austria | Country: Austria | Arrival and Departure: |
| Pedro Duarte | University: Universidade de Lisboa | Country: Portugal | Arrival and Departure: Apr 3 - Apr 16 |
| Håkan Eliasson (Organizer) | University: Université Paris-Cité | Country: France | Arrival and Departure: Feb 20 - Apr 28 |
| Hélène Eynard-Bontemps | University: University of Georgia | Country: United States | Arrival and Departure: Apr 9 - Apr 14 |
| Gerard Farré Puiggalí | University: Universitat Politècnica de Catalunya (UPC) | Country: Spain | Arrival and Departure: Mar 18 - Apr 28 |
| Jordi-Lluis Figueras | University: Uppsala University | Country: Sweden | Arrival and Departure: Jan 18 - Apr 28 |
| Giovanni Forni | University: University of Maryland, College park | Country: United States | Arrival and Departure: Apr 8 - Apr 28 |
| Denis Gaidashev | University: Uppsala University | Country: Sweden | Arrival and Departure: Jan 28 - Apr 28 |
| Arek Goetz | University: San Francisco State University | Country: United States | Arrival and Departure: Mar 20 - Apr 7 |
| Philipp Gohlke | University: Lund University | Country: Sweden | Arrival and Departure: Mar 22 - Mar 31 |
| Anton Gorodetski | University: University of California Irvine | Country: United States | Arrival and Departure: Mar 26 - Apr 28 |
| Jacek Graczyk | University: University Paris Sud | Country: France | Arrival and Departure: Apr 26 - Apr 29 |
| Pablo Gutiérrez Barrientos | University: Universidade Federal Fluminense | Country: Brazil | Arrival and Departure: Apr 22 - Apr 29 |
| Mathieu Helfter | University: IMJ - PRG Jussieu | Country: France | Arrival and Departure: Apr 10 - Apr 16 |
| Michael Jakobson (Online) | University: University of Maryland | Country: United States | Arrival and Departure: |
| Vadim Kaloshin | University: Institute of Science and Technology Austria | Country: Austria | Arrival and Departure: Apr 9 - Apr 12 |
| Davit Karagulyan | University: KTH Royal Institute of Technology | Country: Sweden | Arrival and Departure: Jan 18 - Apr 18 |
| Konstantin Khanin | University: University of Toronto | Country: Canada | Arrival and Departure: Apr 1 - Apr 15 |
| Silvius Klein | University: Pontifical Catholic University of Rio de Janeiro (PUC-Rio) | Country: Brazil | Arrival and Departure: Mar 29 - Apr 18 |
| Raphaël Krikorian (Organizer) | University: École Polytechnique | Country: France | Arrival and Departure: Feb 26 - Mar 15 |
| Georgios Lamprinakis | University: Lund University | Country: Sweden | Arrival and Departure: Mar 15 - Mar 31 |
| Patrice Le Calvez | University: Sorbonne Université | Country: France | Arrival and Departure: Apr 10 - Apr 20 |
| Dongchen Li (Online) | University: Imperial College London | Country: United Kingdom | Arrival and Departure: Mar 31 - Apr 28 |
| Carlangelo Liverani | University: University of Rome Tor Vergata | Country: Italy | Arrival and Departure: Feb 12 - Feb 27 |
| Mikhail Lyubich | University: Stony Brook University | Country: United States | Arrival and Departure: Apr 2 - Apr 26 |
| Tere M- Seara | University: Universitat Politècnica de Catalunya | Country: Spain | Arrival and Departure: Mar 20 - Mar 31 |
| Stefano Marmi | University: Scuola Normale Superiore | Country: Italy | Arrival and Departure: Apr 4 - Apr 28 |
| Marco Martens | University: Stony Brook University | Country: United States | Arrival and Departure: Jan 18 - Apr 28 |
| David Martí-Pete | University: University of Liverpool | Country: United Kingdom | Arrival and Departure: Feb 6 - Feb 27 |
| Michal Misiurewicz | University: Indiana University-Purdue University Indianapolis | Country: United States | Arrival and Departure: Mar 1 - Mar 31 |
| Reza Mohammadpour | University: Uppsala University | Country: Sweden | Arrival and Departure: Jan 24 - Apr 28 |
| Andrès Ignacio Navas Flores | University: University of Santiago | Country: Chile | Arrival and Departure: Apr 9 - Apr 14 |
| Liviana Palmisano | University: KTH Royal Institute of Technology | Country: Sweden | Arrival and Departure: Jan 18 - Apr 28 |
| Yi Pan | University: Institute of Science and Technology Austria | Country: Austria | Arrival and Departure: Feb 26, Apr 9 - Mar 18, Apr 18 |
| Ricardo Perez-Marco | University: CNRS | Country: France | Arrival and Departure: Apr 1 - Apr 25 |
| Tomas Persson | University: Lund University | Country: Sweden | Arrival and Departure: Mar 6 - Mar 17 |
| Yakov Pesin (Online) | University: Pennsylvania State University | Country: United States | Arrival and Departure: |
| Boris Petkovic | University: KTH Royal Institute of Technology | Country: Sweden | Arrival and Departure: Jan 17 - Apr 30 |
| Rafael Potrie (Online) | University: Universidad de la República | Country: Uruguay | Arrival and Departure: |
| Enrique Pujals (Online) | University: Graduate Center- CUNY | Country: United States | Arrival and Departure: |
| Remus Radu | University: Institute of Mathematics of the Romanian Academy | Country: Romania | Arrival and Departure: Jan 21 - Mar 26 |
| Kirthana Rajasekar | University: KTH Royal Institute of Technology, Stockholm | Country: Sweden | Arrival and Departure: Jan 18 - Apr 28 |
| Michal Rams | University: IMPAN | Country: Poland | Arrival and Departure: Feb 13 - Feb 26 |
| Ana Rodrigues (Organizer) | University: University of Exeter | Country: United Kingdom | Arrival and Departure: Jan 18 - Apr 28 |
| Federico Rodriguez Hertz | University: Penn State University | Country: United States | Arrival and Departure: Jan 21 - Jan 29 |
| Jana Rodriguez Hertz | University: Southern University of Science and Technology | Country: China | Arrival and Departure: Jan 17 - Jan 29 |
| Sven Sandfeldt | University: KTH Royal Institute of Technology | Country: Sweden | Arrival and Departure: Jan 18 - Apr 28 |
| Maria Saprykina | University: KTH Royal Institute of Technology | Country: Sweden | Arrival and Departure: Jan 18 - Apr 28 |
| Jörg Schmeling | University: Lund University | Country: Sweden | Arrival and Departure: Mar 1 - Mar 31 |
| Kevin Smith | University: University of Exeter | Country: United Kingdom | Arrival and Departure: Jan 24 - Apr 28 |
| Raluca Tanase | University: Institute of Mathematics of the Romanian Academy | Country: Romania | Arrival and Departure: Jan 21 - Mar 26 |
| Zhuang Tao | University: KTH Royal Institute of Technology | Country: Sweden | Arrival and Departure: Jan 17 - Apr 28 |
| Frank Trujillo | University: University of Zurich | Country: Switzerland | Arrival and Departure: Apr 4 - Apr 19 |
| Warwick Tucker | University: Monash University | Country: Australia | Arrival and Departure: Apr 3 - Apr 9 |
| Dmitry Turaev | University: Imperial College London | Country: United Kingdom | Arrival and Departure: Apr 9 - Apr 18 |
| Corinna Ulcigrai | University: University of Zurich | Country: Switzerland | Arrival and Departure: Apr 11 - Apr 14 |
| Raul Ures | University: Southern University of Science and Technology | Country: China | Arrival and Departure: Jan 17 - Jan 29 |
| Sandro Vaienti | University: Universty of Toulon and Center of Theoretical Physics, Marseille | Country: France | Arrival and Departure: Mar 18 - Apr 3 |
| Paulo Varandas | University: Federal University of Bahia / CMUP - University of Porto | Country: Brazil / Portugal | Arrival and Departure: Mar 27 - Apr 7 |
| Marcelo Viana | University: IMPA | Country: Brazil | Arrival and Departure: |
| Jonguk Yang | University: University of Zurich | Country: Switzerland | Arrival and Departure: Jan 24 - Apr 28 |
| Zhiyuan Zhang | University: CNRS and Universite Sorbonne Paris Nord | Country: France | Arrival and Departure: Apr 10 - Apr 16 |