K-mixing for aperiodic Lorentz gases

2026/07/27 by Giovanni Canestrari, Marco Lenci
#math.DS

paper · pdf

Abstract

We prove a general theorem on the decomposition into K-mixing components for recurrent, piecewise-smooth hyperbolic maps in two dimensions. In contrast with classical results, we do not assume that the map preserves a probability measure. As an application, we show that every recurrent aperiodic Lorentz gas satisfying certain uniformity assumptions is K-mixing. Finally, we discuss some consequences of K-mixing for the decay of correlations relative to zero-mean L¹ observables in aperiodic Lorentz gases.

Citations

• Global-local mixing for infinite measure dynamical systems
• Horocycle flows on abelian covers of surfaces of negative curvature
• Uniformly global observables for 1D maps with an indifferent fixed point
• On asymptotic expansions of ergodic integrals for \Z^d-extensions of translation flows
• Strong mixing for the periodic Lorentz gas flow with infinite horizon
• Abelian covers of hyperbolic surfaces: equidistribution of spectra and infinite volume mixing asymptotics for horocycle flows
• Quantitative global-local mixing for accessible skew products
• Dispersing Fermi-Ulam Models
• Infinite measure mixing for some mechanical systems
• Exactness of the Euclidean algorithm and of the Rauzy induction on the space of interval exchange transfomations
• Ergodicity in Hamiltonian systems

Related

• Strong mixing for the periodic Lorentz gas flow with infinite horizon
• Aperiodic Lorentz gas: recurrence and ergodicity
• Mixing for some non-uniformly hyperbolic systems
• Quenched decay of correlations for one dimensional random Lorenz maps
• Infinite measure mixing for some mechanical systems