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

Published online by Cambridge University Press:  09 March 2004

LEONID POLTEROVICH  and
ZEEV RUDNICK
LEONID POLTEROVICH
Affiliation:
School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel (e-mail: polterov@math.tau.ac.il, rudnick@math.tau.ac.il)
ZEEV RUDNICK
Affiliation:
School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel (e-mail: polterov@math.tau.ac.il, rudnick@math.tau.ac.il)
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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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 24 , Issue 2 , April 2004 , pp. 609 - 619
Copyright
2004 Cambridge University Press

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