arXiv:math/0009143 Abstract

arXiv:math/0009143 [math.DS]Abstract References Reviews Resources

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

Published 2000-09-14, updated 2003-07-14Version 2

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 quasimorphisms of the modular group.

Comments: Final version, accepted for publication in Ergodic Theory & Dynamical Systems

Categories: math.DS, math-ph, math.GR, math.MP, math.NT

Subjects: 37Axx, 11F06, 20F69

Keywords: modular group, cat map, stable mixing, quasi-morphisms, strong chaotic dynamical properties

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