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Article Dans Une Revue Boletim da Sociedade Brasileira de Matemática Année : 2010

Totally dissipative measures for the shift and conformal σ-finite measures for the stable holonomies

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Résumé

In this paper we investigate some results of ergodic theory with infinite measures for a subshift of finite type. We give an explicit way to construct σ-finite measures which are quasi-invariant by the stable holonomy and equivalent to the conditional measures of some σ-invariant measure. These σ-invariant measures are totally dissipative, σ-finite but satisfy a Birkhoff Ergodic-like Theorem. The constructions are done for the symbolic case, but can be extended for uniformly hyperbolic flows or diffeomorphisms.
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hal-02915272 , version 1 (14-08-2020)

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  • HAL Id : hal-02915272 , version 1

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Renaud Leplaideur. Totally dissipative measures for the shift and conformal σ-finite measures for the stable holonomies. Boletim da Sociedade Brasileira de Matemática, 2010. ⟨hal-02915272⟩
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