Map Lattices coupled by collisions

TL;DR

This paper introduces a novel coupled map lattice model where interactions occur through rare, strong collisions, and proves key statistical properties such as uniqueness of the SRB measure and exponential decay of correlations.

Contribution

It presents a new collision-based coupling mechanism for map lattices and establishes fundamental statistical properties for this model.

Findings

Uniqueness of the SRB measure for the model

Exponential decay of correlations in space and time

New theoretical framework for collision-driven dynamics

Abstract

We introduce a new coupled map lattice model in which the weak interaction takes place via rare "collisions". By "collision" we mean a strong (possibly discontinuous) change in the system. For such models we prove uniqueness of the SRB measure and exponential space-time decay of correlations.