Dispersing billiards with moving scatterers

Abstract

We propose a model of Sinai billiards with moving scatterers, in which the locations and shapes of the scatterers may change by small amounts between collisions. Our main result is the exponential loss of memory of initial data at uniform rates, and our proof consists of a coupling argument for non-stationary compositions of maps similar to classical billiard maps. This can be seen as a prototypical result on the statistical properties of time-dependent dynamical systems.

39 pages, 3 figures. (Minor improvements/corrections in this version; to appear in Communications in Mathematical Physics.)

References in corpus (2)

• A central limit theorem for time-dependent dynamical systems
• Non-stationary compositions of Anosov diffeomorphisms

Cited by in corpus (10)

• Quasistatic dynamical systems
• Quasistatic dynamics with intermittency
• Loss of memory and moment bounds for nonstationary intermittent dynamical systems
• Equilibrium states for non-transitive random open and closed dynamical systems
• Sunklodas' approach to normal approximation for time-dependent dynamical systems
• Central limit theorems with a rate of convergence for time-dependent intermittent maps
• An almost sure ergodic theorem for quasistatic dynamical systems
• Projective Cones for Sequential Dispersing Billiards
• Non-stationary Almost Sure Invariance Principle for Hyperbolic Systems with Singularities
• Decay of Correlations for Unbounded Observables