https://hal-unc.archives-ouvertes.fr/hal-02915272Leplaideur, RenaudRenaudLeplaideurLMBA - Laboratoire de Mathématiques de Bretagne Atlantique - UBS - Université de Bretagne Sud - UBO - Université de Brest - CNRS - Centre National de la Recherche ScientifiqueTotally dissipative measures for the shift and conformal σ-finite measures for the stable holonomiesHAL CCSD2010holonomyshiftσ-finite measureholedotted-systemGibbs statesreturn time[MATH.MATH-DS] Mathematics [math]/Dynamical Systems [math.DS][SDU] Sciences of the Universe [physics]Leplaideur, Renaud2020-08-14 05:57:062023-03-24 14:53:182020-08-17 14:22:13enJournal articlesapplication/pdf1In 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.