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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/59935It 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.Final version, accepted for publication in Ergodic Theory & Dynamical SystemsDynamical SystemsMathematical PhysicsGroup TheoryNumber Theory(2000) 37Axx (Primary) 11F06, 20F69 (Secondary)Stable mixing for cat maps and quasi-morphisms of the modular grouptext