Perturbation theory for the topological pressure in analytic dynamical systems

dc.contributor.authorMichalski, Milosz R.en
dc.contributor.committeechairSlaway, Josephen
dc.contributor.committeecochairZweifel, Paul F.en
dc.contributor.committeememberHagedorn, George A.en
dc.contributor.committeememberKlaus, Martinen
dc.contributor.committeememberStreater, R. F.en
dc.contributor.committeememberThompson, James C.en
dc.contributor.departmentMathematicsen
dc.date.accessioned2014-03-14T21:20:48Zen
dc.date.adate2005-10-12en
dc.date.available2014-03-14T21:20:48Zen
dc.date.issued1990en
dc.date.rdate2005-10-12en
dc.date.sdate2005-10-12en
dc.description.abstractWe develop a systematic approach to the problem of finding the perturbative expansion for the topological pressure for an analytic expanding dynamics (/, M) on a Riemannian manifold M. The method is based on the spectral analysis of the transfer operator C. We show that in typical cases, when / depends real-analytically on a set of perturbing parameters ,", the related operators C~ form an analytic family. This gives rise to the rigorous construction of the power series expansion for the pressure via the analytic perturbation theory for eigenvalues, [Kato]. Consequently, the pressure and related dynamical indices, such as dimension spectra, Lyapunov exponents, escape rates and Renyi entropies inherit the real-analyticity in ~ from (I,M).en
dc.description.degreePh. D.en
dc.format.extentviii, 94 leavesen
dc.format.mediumBTDen
dc.format.mimetypeapplication/pdfen
dc.identifier.otheretd-10122005-134403en
dc.identifier.sourceurlhttp://scholar.lib.vt.edu/theses/available/etd-10122005-134403/en
dc.identifier.urihttp://hdl.handle.net/10919/39745en
dc.language.isoenen
dc.publisherVirginia Techen
dc.relation.haspartLD5655.V856_1990.M545.pdfen
dc.relation.isformatofOCLC# 22252269en
dc.rightsIn Copyrighten
dc.rights.urihttp://rightsstatements.org/vocab/InC/1.0/en
dc.subject.lccLD5655.V856 1990.M545en
dc.subject.lcshDifferentiable dynamical systems -- Researchen
dc.titlePerturbation theory for the topological pressure in analytic dynamical systemsen
dc.typeDissertationen
dc.type.dcmitypeTexten
thesis.degree.disciplineMathematicsen
thesis.degree.grantorVirginia Polytechnic Institute and State Universityen
thesis.degree.leveldoctoralen
thesis.degree.namePh. D.en
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