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Spectrum and Statistical Properties of Chaotic Dynamics

  • Conference paper
European Congress of Mathematics

Part of the book series: Progress in Mathematics ((PM,volume 201))

Abstract

We present new developments on the statistical properties of chaotic dynamical systems. We concentrate on the existence of an ergodic physical (SRB) invariant measure and its mixing properties, in particular decay of its correlation functions for smooth observables. In many cases, there is a connection (via the spectrum of a Ruelle-Perron-Frobenius transfer operator) with the analytic properties of a weighted dynamical zeta function, weighted dynamical Lefschetz function, or dynamical Ruelle-Fredholm determinant, built using the periodic orbit structure of the map.

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Authors and Affiliations

  1. CNRS UMR 8628, Université de Paris-Sud, F-91405, Orsay, France

    Viviane Baladi

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  1. Viviane Baladi
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Editors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain

    Carles Casacuberta  & Joan Verdera  & 

  2. Departament d’Algebra i Geometria Facultat de Matemàtiques, Universitat de Barcelona, 08007, Barcelona, Spain

    Rosa Maria Miró-Roig

  3. Departament de Matemàtica Aplicada II, Universitat Politècnica de Catalunya, 08028, Barcelona, Spain

    Sebastià Xambó-Descamps

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Baladi, V. (2001). Spectrum and Statistical Properties of Chaotic Dynamics. In: Casacuberta, C., Miró-Roig, R.M., Verdera, J., Xambó-Descamps, S. (eds) European Congress of Mathematics. Progress in Mathematics, vol 201. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8268-2_11

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