We study one-dimensional lattices of weakly coupled piecewise expanding interval maps as dynamical systems. Since the local maps are not required to have full branches and the coupling map is not required to be a homeomorphism of the infinite-dimensional state space, we cannot use symbolic dynamics or other techniques from statistical mechanics. Instead we prove that the transfer operator of the infinite-dimensional system has a spectral gap on suitable Banach spaces generated by measures with marginals that have densities of bounded variation. This implies, in particular, exponential decay of correlations in time and space.
Keller, G., Liverani, C. (2004). A spectral gap for a one-dimensional lattice of coupled piecewise expanding interval maps. In J.-R. Chazottes and B. Fernandez (a cura di), Dynamics of coupled map lattices and of related spatially extended systems (pp. 115-151). Berlin : Springer.
A spectral gap for a one-dimensional lattice of coupled piecewise expanding interval maps
LIVERANI, CARLANGELO
2004-07-01
Abstract
We study one-dimensional lattices of weakly coupled piecewise expanding interval maps as dynamical systems. Since the local maps are not required to have full branches and the coupling map is not required to be a homeomorphism of the infinite-dimensional state space, we cannot use symbolic dynamics or other techniques from statistical mechanics. Instead we prove that the transfer operator of the infinite-dimensional system has a spectral gap on suitable Banach spaces generated by measures with marginals that have densities of bounded variation. This implies, in particular, exponential decay of correlations in time and space.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
