Ruelle Perron Frobenius spectrum for Anosov maps
نویسندگان
چکیده
منابع مشابه
Ruelle-perron-frobenius Spectrum for Anosov Maps
We extend a number of results from one dimensional dynamics based on spectral properties of the Ruelle-Perron-Frobenius transfer operator to Anosov diffeomorphisms on compact manifolds. This allows to develop a direct operator approach to study ergodic properties of these maps. In particular, we show that it is possible to define Banach spaces on which the transfer operator is quasicompact. (In...
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To study the convergence to equilibrium in random maps, we develop the spectral theory of the corresponding transfer (Perron— Frobenius) operators acting in a certain Banach space of generalized functions (distributions). The random maps under study in a sense fill the gap between expanding and hyperbolic systems, since among their (deterministic) components there are both expanding and contrac...
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متن کاملFredholm Determinants, Anosov Maps and Ruelle Resonances
I show that the dynamical determinant, associated to an Anosov diffeomorphism, is the Fredholm determinant of the corresponding RuellePerron-Frobenius transfer operator acting on appropriate Banach spaces. As a consequence it follows, for example, that the zeroes of the dynamical determinant describe the eigenvalues of the transfer operator and the Ruelle resonances and that, for C∞ Anosov diff...
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ژورنال
عنوان ژورنال: Nonlinearity
سال: 2002
ISSN: 0951-7715
DOI: 10.1088/0951-7715/15/6/309