We consider the $(d+1)$-dimensional an dynamical system constituted by weakly coupled expanding circle maps on $\Z^d$ together with the spatial shifts. This viewpoint allows us to use thermodynamic formalism, and to describe the asymptotic behavior of the system in this setup. We obtain a volume lemma, which describes the exponential behavior of the size under Lebesgue measure of dynamical balls around any orbit, and then a large deviations principle for the empirical measure associated to this dynamical system. The proofs are direct: we do not use the coding constructed by Jiang for such systems.
Publié le : 2004-01-14
Classification:
Coupled map lattices,
large deviations,
thermodynamic formalism,
60F10,
37A50,
37L60
@article{1079021461,
author = {Bardet, Jean-Baptiste and Ben Arous, G\'erard},
title = {Spatio-temporal large deviations principle for coupled circle maps},
journal = {Ann. Probab.},
volume = {32},
number = {1A},
year = {2004},
pages = { 692-729},
language = {en},
url = {http://dml.mathdoc.fr/item/1079021461}
}
Bardet, Jean-Baptiste; Ben Arous, Gérard. Spatio-temporal large deviations principle for coupled circle maps. Ann. Probab., Tome 32 (2004) no. 1A, pp. 692-729. http://gdmltest.u-ga.fr/item/1079021461/