Diophantine approximation, fractal sets and lacunary sequences

Fractal Geometry and Dynamics

27 September 15:00 - 15:50

Sanju Velani - University of York

The metric theory of Diophantine approximation on fractal sets is discussed in which the denominators of the rational approximates are restricted to lacunary sequences. The case of the standard middle third Cantor set and the sequence {3^n : n \in N} is the starting point of our investigation. Our metric results for this simple setup answers a problem raised by Mahler. As with all ‘good’ problems – its solution opens up a can of worms.
Kenneth J. Falconer
University of St Andrews
Maarit Järvenpää
University of Oulu
Antti Kupiainen
University of Helsinki
Francois Ledrappier
University of Notre Dame
Pertti Mattila
University of Helsinki


Maarit Järvenpää


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