# Map Lattices Coupled by Collisions

@article{Keller2008MapLC, title={Map Lattices Coupled by Collisions}, author={Gerhard Keller and Carlangelo Liverani}, journal={Communications in Mathematical Physics}, year={2008}, volume={291}, pages={591-597} }

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.

#### 11 Citations

0 A pr 2 02 1 MAP LATTICES COUPLED BY COLLISIONS : HITTING TIME STATISTICS AND COLLISIONS

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Abstract. We study map lattices coupled by collision and show how perturbations of transfer operators associated with the spatially periodic approximation of the model can be used to extract… Expand

Rare events, exponential hitting times and extremal indices via spectral perturbation†

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We discuss how an eigenvalue perturbation formula for transfer operators of dynamical systems is related to exponential hitting time distributions and extreme value theory for processes generated by… Expand

Condensation versus independence in weakly interacting CMLs

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On the Limiting Markov Process of Energy Exchanges in a Rarely Interacting Ball-Piston Gas

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We analyse the process of energy exchanges generated by the elastic collisions between a point-particle, confined to a two-dimensional cell with convex boundaries, and a ‘piston’, i.e. a… Expand

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We investigate dynamical systems obtained by coupling two maps, one of which is chaotic and is exemplified by an Anosov diffeomorphism, and the other is of gradient type and is exemplified by a… Expand

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In this paper we present a rigorous analysis of a class of coupled dynamical systems in which two distinct types of components, one excitatory and the other inhibitory, interact with one another.… Expand

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Map lattices coupled by collisions: hitting time statistics and collisions per lattice unit

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- 2021

Abstract. We study map lattices coupled by collision and show how perturbations of transfer operators associated with the spatially periodic approximation of the model can be used to extract… Expand

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Bismarckstr . 1 1 2 , 91052 Erlangen, Germany E-mail address: keller@mi.uni-erlangen

- Bismarckstr . 1 1 2 , 91052 Erlangen, Germany E-mail address: keller@mi.uni-erlangen