Limit theorems for coupled interval maps - Bardet, Jean-Baptiste; Gouëzel, Sébastien; Keller, Gerhard (Stochastics and Dynamics, 2007)
We prove a local limit theorem for Lipschitz continuous observables on a weakly coupled lattice of piecewise expanding mixing 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 [9] where the ordinary transfer operator was studied. © 2007 World Scientific Publishing Company.
UnivIS-Import:2015-03-09:Pub.2007.nat.dma.pma29.limitt
Keywords: Coupled map lattice; Local limit theorem; Piecewise expanding map; Spectral gap