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001440154 020__ $$a9783030748630$$q(electronic bk.)
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001440154 020__ $$z9783030748623$$q(print)
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001440154 0247_ $$a10.1007/978-3-030-74863-0$$2doi
001440154 035__ $$aSP(OCoLC)1273350946
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001440154 049__ $$aISEA
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001440154 08204 $$a515/.48$$223
001440154 24500 $$aThermodynamic formalism :$$bCIRM Jean-Morlet Chair, Fall 2019 /$$cMark Pollicott, Sandro Vaienti, editors.
001440154 264_1 $$aCham, Switzerland :$$bSpringer,$$c2021.
001440154 300__ $$a1 online resource (xiv, 536 pages) :$$billustrations (some color)
001440154 336__ $$atext$$btxt$$2rdacontent
001440154 337__ $$acomputer$$bc$$2rdamedia
001440154 338__ $$aonline resource$$bcr$$2rdacarrier
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001440154 4901_ $$aLecture notes in mathematics,$$x1617-9692 ;$$vvolume 2290
001440154 4900_ $$aCIRM Jean-Morlet series
001440154 5050_ $$aIntro -- Foreword -- Preface -- Contents -- Contributors -- Part I Specifications and Expansiveness -- 1 Beyond Bowen's Specification Property -- 1.1 Introduction -- 1.2 Main Ideas: Uniqueness of the Measure of Maximal Entropy -- 1.2.1 Entropy and Thermodynamic Formalism -- 1.2.2 Bowen's Original Argument: The Symbolic Case -- 1.2.2.1 The Specification Property in a Shift Space -- 1.2.2.2 The Lower Gibbs Bound as the Mechanism for Uniqueness -- 1.2.2.3 Building a Gibbs Measure -- 1.2.3 Relaxing Specification: Decompositions of the Language -- 1.2.3.1 Decompositions
001440154 5058_ $$a1.2.3.2 An Example: Beta Shifts -- 1.2.3.3 Periodic Points -- 1.2.4 Beyond Shift Spaces: Expansivity in Bowen's Argument -- 1.2.4.1 Topological Entropy -- 1.2.4.2 Expansivity -- 1.2.4.3 Specification -- 1.2.4.4 Bowen's Proof Revisited -- 1.3 Non-uniform Bowen Hypotheses and Equilibrium States -- 1.3.1 Relaxing the Expansivity Hypothesis -- 1.3.2 Derived-from-Anosov Systems -- 1.3.2.1 Construction of the Mañé Example -- 1.3.2.2 Estimating the Entropy of Obstructions -- 1.3.2.3 Specification for Mañé Examples -- 1.3.3 The General Result for MMEs in Discrete-Time
001440154 5058_ $$a1.3.4 Partially Hyperbolic Systems with One-Dimensional Center -- 1.3.4.1 A Small Collection of Obstructions -- 1.3.4.2 A Good Collection with Specification -- 1.3.5 Unique Equilibrium States -- 1.3.5.1 Topological Pressure -- 1.3.5.2 Regularity of the Potential Function: The Bowen Property -- 1.3.5.3 The Most General Discrete-Time Result -- 1.3.5.4 Partial Hyperbolicity -- 1.4 Geodesic Flows -- 1.4.1 Geometric Preliminaries -- 1.4.1.1 Overview -- 1.4.1.2 Surfaces -- 1.4.1.3 Invariant Foliations via Horospheres -- 1.4.1.4 Jacobi Fields and Local Construction of Stables/Unstables
001440154 5058_ $$a1.4.2 Equilibrium States for Geodesic Flows -- 1.4.2.1 The General Uniqueness Result for Flows -- 1.4.2.2 Geodesic Flows in Non-positive Curvature -- 1.4.2.3 Uniqueness Can Fail Without a Pressure Gap -- 1.4.2.4 Uniqueness Given a Pressure Gap -- 1.4.2.5 Pressure and Periodic Orbits -- 1.4.2.6 Main Ideas of the Proof of Uniqueness -- 1.4.2.7 Unique MMEs for Surfaces Without Conjugate Points -- 1.4.2.8 Geodesic Flows on Metric Spaces -- 1.4.3 Kolmogorov Property for Equilibrium States -- 1.4.3.1 Moving Up the Mixing Hierarchy -- 1.4.3.2 Ledrappier's Approach -- 1.4.3.3 Decompositions for Products
001440154 5058_ $$a1.4.3.4 Expansivity Issues -- 1.4.4 Knieper's Entropy Gap -- 1.4.4.1 Entropy in the Singular Set -- 1.4.4.2 Warm-Up: Shifts with Specification -- 1.4.4.3 Entropy Gap for Geodesic Flow -- 1.4.4.4 Other Applications of Pressure Production -- References -- 2 The Role of Continuity and Expansiveness on Leo and Periodic Specification Properties -- 2.1 Introduction -- 2.2 Definitions -- 2.3 Proofs -- 2.3.1 Proof of Theorem 1.2 -- 2.3.2 Proof of Theorem 1.3 -- 2.3.3 Proof of Theorem 1.4 -- 2.4 Examples -- References -- Part II Low Dimensional Dynamics and Thermodynamics Formalism
001440154 506__ $$aAccess limited to authorized users.
001440154 520__ $$aThis 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
001440154 588__ $$aOnline resource; title from PDF title page (SpringerLink, viewed October 5, 2021).
001440154 650_0 $$aErgodic theory.
001440154 650_0 $$aFractals.
001440154 650_0 $$aThermodynamics$$xMathematics.
001440154 650_6 $$aThéorie ergodique.
001440154 650_6 $$aFractales.
001440154 650_6 $$aThermodynamique$$xMathématiques.
001440154 655_7 $$aLlibres electrònics.$$2thub
001440154 655_0 $$aElectronic books.
001440154 7001_ $$aPollicott, Mark,$$eeditor.
001440154 7001_ $$aVaienti, Sandro,$$eeditor.
001440154 7102_ $$aCentre de rencontres mathématiques de Luminy.
001440154 77608 $$iPrint version:$$tThermodynamic formalism.$$dCham, Switzerland : Springer, 2021$$z3030748626$$z9783030748623$$w(OCoLC)1243350247
001440154 830_0 $$aLecture notes in mathematics (Springer-Verlag) ;$$v2290.$$x1617-9692
001440154 852__ $$bebk
001440154 85640 $$3Springer Nature$$uhttps://univsouthin.idm.oclc.org/login?url=https://link.springer.com/10.1007/978-3-030-74863-0$$zOnline Access$$91397441.1
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