Limit theorems for coupled interval maps

Jean-Baptiste Bardet (1) , Sébastien Gouëzel (1) , Gerhard Keller (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Mathematisches Institut, Universität Erlangen

We prove a local limit theorem for Lipschitz continuous observables on a weakly coupled lattice of piecewise expanding interval maps. The core of the paper is a proof that the spectral radii of the Fourier-transfer operators for such a system are strictly less than $1$. This extends the approach of [KL2] where the ordinary transfer operator was studied.

Mots clés: Coupled map lattice; piecewise expanding map; spectral gap; local limit theorem

Domaines: Systèmes dynamiques [math.DS]

Jean-Baptiste Bardet, Sébastien Gouëzel, Gerhard Keller. Limit theorems for coupled interval maps. Stochastics and Dynamics, 2007, 7 (1), pp.17-36. ⟨hal-00097783⟩