Multifractal analysis for Bedford-McMullen carpets (2009)
In this paper we compute the multifractal analysis for local dimensions of Bernoulli measures supported on the self-affine carpets introduced by Bedford-McMullen. This extends the work of King where...
Lyapunov spectrum for rational maps (2008)
Gelfert, Katrin, Przytycki, Feliks, Rams, Michal
We study the dimension spectrum of Lyapunov exponents for rational maps on the Riemann sphere.
Multifractal analysis of weak Gibbs measures for non-uniformly expanding C^1 maps (2008)
We consider the local dimension spectrum of a weak Gibbs measure on a C^1 non-uniformly hyperbolic system of Manneville- Pomeau type. We present the spectrum in three ways: using invariant measures,...
The Lyapunov spectrum of some parabolic systems (2007)
We study the Hausdorff dimension spectrum for Lyapunov exponents for a class of interval maps which includes several non-hyperbolic situations. We also analyze the level sets of points with given...
Jaroszewska, Joanna, Rams, Michal
We consider measures which are invariant under a measurable iterated function system with positive, place-dependent probabilities in a separable metric space. We provide an upper bound of the...
Growth rates for geometric complexities and counting functions in polygonal billiards (2007)
We introduce a new method for estimating the growth of various quantities arising in dynamical systems. We apply our method to polygonal billiards on surfaces of constant curvature. For instance, we...
Generic behavior of iterated function systems with overlaps (2005)
Abstract We prove that for typical self-similar iterated function systems satisfying the transversality condition the number of intersections of cylinders of a given size is for many sizes nearly as...
Generic behavior of iterated function systems with overlaps (2005)
Abstract We prove that for typical self-similar iterated function systems satisfying the transversality condition the number of intersections of cylinders of a given size is for many sizes nearly as...