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

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

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.

Leonid Polterovich | Zeev Rudnick

[1] M. Baake,et al. Reversing symmetry group of Gl ( 2 , Z ) and PGl ( 2 , Z ) matrices with connections to cat maps and trace maps , 1997 .

[2] 藤原耕二. Bounded cohomology of subgroups of mapping class groups (双曲空間及び離散群の研究研究集会報告集) , 2001 .

[3] M. Baake,et al. Reversing symmetry group of and matrices with connections to cat maps and trace maps , 1997 .

[4] D. Epstein,et al. The second bounded cohomology of word-hyperbolic groups , 1997 .

[5] É. Ghys,et al. Surfaces et cohomologie bornée , 1988 .

[6] P. Heywood. Trigonometric Series , 1968, Nature.

[7] A. Beardon. The Geometry of Discrete Groups , 1995 .

[8] John G. Ratcliffe,et al. Geometry of Discrete Groups , 2019, Foundations of Hyperbolic Manifolds.

[9] M. Burger,et al. Continuous bounded cohomology and applications to rigidity theory , 2001 .

[10] M. Burger,et al. Bounded cohomology of lattices in higher rank Lie groups , 1999 .

[11] G. Keller,et al. BOUNDED ELEMENTARY GENERATION OF SL,n (0) , 1983 .

[12] Kick stability in groups and dynamical systems , 2000, math/0005031.

[13] Jacqueline Grennon. , 2nd Ed. , 2002, The Journal of nervous and mental disease.