Stable mixing for cat maps and quasi-morphisms of the modular group

Leonid Polterovich, Zeév Rudnick

Type: Article

Publication Date: 2004-03-09

Citations: 29

DOI: https://doi.org/10.1017/s0143385703000531

Abstract

It is well known that the action of a hyperbolic element ('cat map') of the modular group on the 2-torus has strong chaotic dynamical properties such as mixing and exponential decay of correlations. In this note we study stability of this behaviour with respect to kicks. Our approach is based on geometric group theory, and in particular on a new result on quasi-morphisms of the modular group.

Locations

Ergodic Theory and Dynamical Systems - View
arXiv (Cornell University) - View - PDF

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