Show simple item record

dc.contributor.advisorJAKOBSON, MICHAELen_US
dc.contributor.authorTapia, Adriana Mariaen_US
dc.date.accessioned2014-02-11T06:31:27Z
dc.date.available2014-02-11T06:31:27Z
dc.date.issued2013en_US
dc.identifier.urihttp://hdl.handle.net/1903/14920
dc.description.abstractGibbs measure which are also called Sinai-Ruelle-Bowen Measure describe asymptotic behavior and statistical properties of typical trajectories in many physical systems. In this work we review several methods of studying Gibbs measures by Ya.G. Sinai, D. Ruelle, R. Bowen, and P. Walters. First, using symbolic dynamics we show for subshifts of finite type that the invariant measure obtained in the Ruelle-Perron-Frobenius (R-P-F)Theorem is an ergodic Gibbs measure. Second, the proof of the R-P-F theorem is given following Walters approach, where he considers maps with infinitely many branches. In both cases, the idea is to find a fixed point of the transfer operator which will allow us to define the measure μ . Ergodic properties of μ are studied. In particular results are valid for expanding maps. These ideas are illustrated in the example of an expanding map with two branches where we show explicitly the existence of an invariant measure as well as we prove ergodicity, exactness, and the Rochlin Entropy formula.en_US
dc.language.isoenen_US
dc.titleERGODIC PROPERTIES OF GIBBS MEASURES FOR EXPANDING MAPSen_US
dc.typeThesisen_US
dc.contributor.publisherDigital Repository at the University of Marylanden_US
dc.contributor.publisherUniversity of Maryland (College Park, Md.)en_US
dc.contributor.departmentMathematicsen_US
dc.subject.pqcontrolledMathematicsen_US
dc.subject.pquncontrolledERGODICen_US
dc.subject.pquncontrolledGIBBSen_US
dc.subject.pquncontrolledINVARIANTen_US


Files in this item

Thumbnail

This item appears in the following Collection(s)

Show simple item record