Virginia Tech
Perturbation theory for the topological pressure in analytic dynamical systems
Abstract
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).
Degree
thesis:*- Name thesis:degree_name
- Ph. D.
- Level thesis:degree_level
- doctoral
- Discipline thesis:degree_discipline
- Mathematics
- Department dc:contributor.department
- Mathematics
- Grantor dc:publisher
- Virginia Tech
- Year dc:date.issued
- 1990
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Michalski, Milosz R.
- Chairs dc:contributor.committeechair
-
- Slaway, Joseph
- Zweifel, Paul F.
- Committee members dc:contributor.committeemember
-
- Hagedorn, George A.
- Klaus, Martin
- Streater, R. F.
- Thompson, James C.
Rights
dc:rights- Statement dc:rights
-
- In Copyright
- Licence dc:rights.uri
- Language dc:language.iso
- en
Identifiers
dc:identifier.*- Dc Identifier Other
- etd-10122005-134403
- OAI identifier oai:identifier
- oai:vtechworks.lib.vt.edu:10919/39745