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Correlation decay for Markov maps on a countable state space

Published online by Cambridge University Press:  26 March 2001

VÉRONIQUE MAUME-DESCHAMPS
VÉRONIQUE MAUME-DESCHAMPS
Affiliation:
Laboratoire de Topologie, Université de Bourgogne – UMR 5584 du CNRS, 9, Avenue Alain Savary, BP 47870, 21078 Dijon Cedex, France (e-mail: [email protected])
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Abstract

We estimate the decay of correlations for some Markov maps on a countable state space. A necessary and sufficient condition is given for the transfer operator to be quasi-compact on the space of locally Lipschitz functions. In the non-quasi-compact case, the decay of correlations depends on the contribution to the transfer operator of the complementary of finitely many cylinders. Estimates are given for some non-uniformly expanding maps and for maps with bounded jumps.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 21 , Issue 1 , February 2001 , pp. 165 - 196
Copyright
© 2001 Cambridge University Press

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