
ISSN:
1930-5311
eISSN:
1930-532X
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Journal of Modern Dynamics
2018 , Volume 13
Roy Adler Memorial Volume edited by Michael Boyle, Brian Marcus, Omri Sarig, and Benjamin Weiss
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We study rational step function skew products over certain rotations of the circle proving ergodicity and bounded rational ergodicity when the rotation number is a quadratic irrational. The latter arises from a consideration of the asymptotic temporal statistics of an orbit as modelled by an associated affine random walk.
We construct countable Markov partitions for non-uniformly hyperbolic diffeomorphisms on compact manifolds of any dimension, extending earlier work of Sarig [
Let
The set of automorphisms of a one-dimensional subshift
An important consequence of the theory of entropy of
We study the smooth self-maps
We study hyperbolic attractors of some dynamical systems with apriori given countable Markov partitions. Assuming that contraction is stronger than expansion, we construct new Markov rectangles such that their cross-sections by unstable manifolds are Cantor sets of positive Lebesgue measure. Using new Markov partitions we develop thermodynamical formalism and prove exponential decay of correlations and related properties for certain Hölder functions. The results are based on the methods developed by Sarig [
We study skew products where the base is a hyperbolic automorphism of
We prove that for every
We show that an arbitrary factor map
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