图书简介
This volume arose from a semester at CIRM-Luminy on “Thermodynamic Formalism: Applications to Probability, Geometry and Fractals” which brought together leading experts in the area to discuss topical problems and recent progress. It includes a number of surveys intended to make the field more accessible to younger mathematicians and scientists wishing to learn more about the area.Thermodynamic formalism has been a powerful tool in ergodic theory and dynamical system and its applications to other topics, particularly Riemannian geometry (especially in negative curvature), statistical properties of dynamical systems and fractal geometry.This work will be of value both to graduate students and more senior researchers interested in either learning about the main ideas and themes in thermodynamic formalism, and research themes which are at forefront of research in this area.
Part I Specification and Expansiveness.- Beyond Bowen’s Specification Property.- The role of continuity and expansiveness on leo and periodic specification properties.- Thermodynamic Formalism and Geometric Applications for Transcendental Meromorphicand Entire Functions.- Statistical properties of periodic points for infinitely renormalizable unimodal maps.- Part II Probability theory, ergodicity and thermodynamic formalism.- Recurrent sets for ergodic sums of an integer valued function.- Almost Sure Invariance Principle for Random Distance Expanding Maps with a NonuniformDecay of Correlations.- Limit theorem for reflected random walks.- The strong Borel–Cantelli property in conventional and nonconventional setups.- Application of the convergence of the spatio-temporal processes for visits to small sets.- Part III Geometry and thermodynamic formalism.- Rate of mixing for equilibrium states in negative curvature and trees.- Statistical properties of the Rauzy-Veech-Zorich map.- Entropy Rigidity, Pressure Metric, and Immersed Surfaces in Hyperbolic 3-Manifolds.- Higher Teichmüller Theory for surface groups and shifts of finite type.- Part IV Fractal Geometry.- Dimension estimates for C1 iterated function systems and C1 repellers, a survey.- Intermediate dimensions - a survey.- Fractal geometry of Bedford-McMullen carpets.- Some variants of Orponen’s theorem on visible parts of fractal sets.
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