Title
Markov extensions for dynamical systems with holes: an application to expanding maps of the interval
Document Type
Article
Article Version
Post-print
Publication Date
2005
Abstract
We introduce the Markov extension, represented schematically as a tower, to the study of dynamical systems with holes. For tower maps with small holes, we prove the existence of conditionally invariant probability measures which are absolutely continuous with respect to Lebesgue measure (abbreviated a.c.c.i.m.). We develop restrictions on the Lebesgue measure of the holes and simple conditions on the dynamics of the tower which ensure existence and uniqueness in a class of Holder continuous densities. We then use these results to study the existence and properties of a.c.c.i.m. forC 1+α expanding maps of the interval with holes. We obtain the convergence of the a.c.c.i.m. to the SRB measure of the corresponding closed system as the measure of the hole shrinks to zero.
Publication Title
Israel Journal of Mathematics
Repository Citation
Demers, Mark, "Markov extensions for dynamical systems with holes: an application to expanding maps of the interval" (2005). Mathematics Faculty Publications. 40.
https://digitalcommons.fairfield.edu/mathandcomputerscience-facultypubs/40
Published Citation
Mark Demers, "Markov extensions for dynamical systems with holes: an application to expanding maps of the interval," Israel Journal of Mathematics 146:1 (2005), 189-221.
DOI
10.1007/BF02773533
Peer Reviewed
Comments
Copyright 2005 Springer Verlag.
The final publication is available at www.springerlink.com