Thermodynamic formalism for piecewise expanding maps in finite dimension

Abstract

We study weighted transfer operators associated to a piecewise expanding map on a compact manifold, and a piecewise Holder weight, acting on Sobolev spaces. We bound the essential spectral radius in terms of a topological pressure for a subadditive potential. Under a new small boundary pressure condition, we improve the estimate by establishing a variational principle for piecewise expanding maps and subadditive potentials. Version v2 is the electronic copy of the version to appear in DCDS

Version v2 is the electronic copy of the version to appear in DCDS

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• Ruelle-Perron-Frobenius spectrum for Anosov maps
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Cited by in corpus (1)

• Discontinuities cause essential spectrum on surfaces