Speaker
Antti Käenmäki, University of Eastern Finland
Abstract
Exponential separation rules out a dimension drop for planar self-conformal sets and measures, by a recent result of Feng and Rapaport, but it is hard to verify for a concrete non-linear system. Bárány, Kolossváry, and Troscheit made it checkable on the real line through a dual iterated function system; the quantity their condition separates is the pre-Schwarzian derivative. I will explain how this carries the construction to the plane and one level higher, to the Schwarzian, and how the resulting conditions are C^2-open and dense, making the absence of a dimension drop C^2-generic in the plane.
Antti Käenmäki, University of Eastern Finland
Abstract
Exponential separation rules out a dimension drop for planar self-conformal sets and measures, by a recent result of Feng and Rapaport, but it is hard to verify for a concrete non-linear system. Bárány, Kolossváry, and Troscheit made it checkable on the real line through a dual iterated function system; the quantity their condition separates is the pre-Schwarzian derivative. I will explain how this carries the construction to the plane and one level higher, to the Schwarzian, and how the resulting conditions are C^2-open and dense, making the absence of a dimension drop C^2-generic in the plane.