arXiv subjects

Michael Jakobson

Publications and source records attributed to Michael Jakobson.

4 recordsLinked to original sources

arXiv2018

Countable Markov Partitions Suitable for Thermodynamic Formalism

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 crossections 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.

math.DS↗

arXiv2016

Thermodynamic formalism for some systems with countable Markov structures

We study ergodic properties of certain piecewise smooth two-dimensional systems by constructing countable Markov partitions. Using thermodynamic formalism we prove exponential decay of correleations.

math.DS↗

arXiv1996

Asymptotic measures for hyperbolic piecewise smooth mappings of a rectangle

We prove the existence of Sinai-Ruelle-Bowen measures for a class of $C^2$ self-mappings of a rectangle with unbounded derivatives. The results can be regarded as a generalization of a well-known one dimensional Folklore Theorem on the existence of absolutely continuous invariant measures. In an earlier paper analogous results were stated and the proofs were sketched for the case of invertible systems. Here we give complete proofs in the more general case of noninvertible systems, and, in particular, develop the theory of stable and unstable manifolds for maps with unbounded derivatives.

math.DS↗

arXiv1991

Quasisymmetric conjugacies between unimodal maps

It is shown that some topological equivalency classes of S-unimodal maps are equal to quasisymmetric conjugacy classes. This includes some infinitely renormalizable polynomials of unbounded type.

math.DS↗