6533b857fe1ef96bd12b4dfd

RESEARCH PRODUCT

Quasi-Stationary Distribution and Gibbs Measure of Expanding Systems

Bernard SchmittPierre ColletServet Martínez

subject

Cantor setPure mathematicssymbols.namesakeTransformation (function)Stationary distributionBounded functionMetric (mathematics)symbolsLimit (mathematics)Gibbs measureExponential functionMathematics

description

Let T be an expanding transformation defined on A —(J A{, i= 1being a finite collection of connected open bounded subsets of 2Rn,such that T Acontains strictly Aand Tis Markovian. We prove the existence of a quasi-stationary distrition for T. We show that the T-invariant probability on the limit Cantor set is Gibbsian with potential Log|_DT|. Using the Hilbert projective metric we prove that both distributions are weak limits of conditional laws of probabilities, the speed of convergence being exponential. These results develop a previous work by G. Pianigiani and J.A. Yorke.

yearjournalcountryeditionlanguage
1996-01-01
https://doi.org/10.1007/978-94-009-0239-8_19