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Regular and Stochastic Behaviour in Dynamical Systems

Thermodynamic formalism for piecewise expanding maps in finite dimension

speaker: Roberto Castorrini (Università di Pisa)

abstract: In the last few years the functional approach to the study of the statistical properties of a dynamical system has been proven extremely successful, especially in the case of hyperbolic systems. One of the main targets is to find a Banach space on which the "non-compact" (essential) part of the spectrum of the associated transfer operator is as small as possible. This translates into finer information on the statistical behaviour of the system. In the smooth hyperbolic case, the best known estimate for the essential spectral radius is obtained by Baladi and Tsujii for micro-local spaces by thermodynamic formalism techniques, as a variational expression for a subadditive topological pressure. In this work we obtain an unconditional estimate for the essential spectral radius of transfer operators associated to piecewise expanding maps on a compact manifold of finite dimension and a piecewise Holder weight, acting on Sobolev spaces. In addition, under a new small boundary pressure condition, we improve the estimate by establishing a variational principle for piecewise expanding maps and subadditive potentials. This is a joint work with Viviane Baladi.

Mon 5 Jun, 14:30 - 15:30, Aula Dini
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