Perturbation theory for the topological pressure in analytic dynamical systems

• Main Author: Michalski, Milosz R.
• Other Authors: Mathematics
• Format: Others
• Language: en
• Published: Virginia Tech 2014
• Subjects: LD5655.V856 1990.M545; Differentiable dynamical systems > Research
• Online Access: http://hdl.handle.net/10919/39745; http://scholar.lib.vt.edu/theses/available/etd-10122005-134403/

We 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). === Ph. D.