- 01-349 Jean-Baptiste Bardet
- Limit theorems for coupled analytic maps
Oct 2, 01
(auto. generated ps),
of related papers
Abstract. In a recent paper, H.H. Rugh gave a new and simpler method to prove
existence of an invariant measure with nice mixing properties for some
weakly coupled analytic maps. He proved in fact a spectral gap property
for a well-defined transfer operator.
We modify this method to construct generalized transfer operators
associated to potentials and preserve the spectral gap for small
potentials. This allows us to prove new limit results for these systems :
Central Limit Theorem, Moderate Deviations Principle and a partial Large
Deviations result. These results are available under wide classes of
observables and initial measures.