Perturbation theory for the topological pressure in analytic dynamical systems

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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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