Markov structures and decay of correlations for non-uniformly expanding dynamical systems☆

By José F. Alves, Stefano Luzzatto, Vilton Pinheiro. 2002

125 citations recorded by the source corpus.

We consider non-uniformly expanding maps on compact Riemannian manifolds of arbitrary dimension, possibly having discontinuities and/or critical sets, and show that under some general conditions they admit an induced Markov tower structure. Moreover, the decay of the return time function can be controlled in terms of the time generic points need to achieve some uniform expanding behavior. As a consequence we obtain some rates for the decay of correlations of those maps and conditions for the validity of the Central Limit Theorem.

Subfields: Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/e778d1eab4303a7d1fe8dd283c88a2a5c10ce334

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

Large Deviations for Non-Uniformly Expanding Maps (2006, background): “Then for the same kind of attracting sets we obtain an upper bound for the subset corresponding to ( 7 ).”
Physical measures and absolute continuity for one-dimensional center direction (2013, background): “Alves, Luzzatto and Pinheiro [7,8] constructed Markov structures and used them to study fine ergodic properties of these maps.”
Hitting time statistics and extreme value theory (2008, background): “Applying [ ALP ] and [G2] together shows that these maps admit a Young tower whose return time tail is related to the volume decay rate of the hyperbolic tail set.”
SRB measures for partially hyperbolic systems whose central direction is weakly expanding (2014, unknown): “…but the same kind of questions, and the Palis conjecture, also apply to endomorphisms—see for example [9, 10, 17, 24, 32, 31] for the setting of one-dimensional maps, [45] in two dimensions, and [5, 6, 40, 41] for the construction of SRB measures in certain higher-dimensional settings.”