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Perturbation theory for the topological pressure in analytic dynamical systems
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 ~