For and , we study weighted transfer operators associated to a piecewise expanding map on a compact manifold of dimension , and a piecewise 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.

Thermodynamic formalism for piecewise expanding maps in finite dimension

Castorrini, Roberto
2024-01-01

Abstract

For and , we study weighted transfer operators associated to a piecewise expanding map on a compact manifold of dimension , and a piecewise 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.
2024
Transfer operator, piecewise expanding map, subadditive thermodynamic formalism, Topological pressure.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12571/33904
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