Equilibrium States In Negative Curvature

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Equilibrium States In Negative Curvature

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Author : Barbara Schapira
language : en
Publisher:
Release Date : 2015

Equilibrium States In Negative Curvature written by Barbara Schapira and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015 with Curvature categories.

With their origin in thermodynamics and symbolic dynamics, Gibbs measures are crucial tools to study the ergodic theory of the geodesic flow on negatively curved manifolds. We develop a framework (through Patterson-Sullivan densities) allowing us to get rid of compactness assumptions on the manifold, and prove many existence, uniqueness and finiteness results of Gibbs measures. We give many applications to the variational principle, the counting and equidistribution of orbit points and periods, the unique ergodicity of the strong unstable foliation and the classification of Gibbs densities on some Riemannian covers

Equidistribution And Counting Under Equilibrium States In Negative Curvature And Trees

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Author : Anne Broise-Alamichel
language : en
Publisher: Springer Nature
Release Date : 2019-12-16

Equidistribution And Counting Under Equilibrium States In Negative Curvature And Trees written by Anne Broise-Alamichel and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-12-16 with Mathematics categories.

This book provides a complete exposition of equidistribution and counting problems weighted by a potential function of common perpendicular geodesics in negatively curved manifolds and simplicial trees. Avoiding any compactness assumptions, the authors extend the theory of Patterson-Sullivan, Bowen-Margulis and Oh-Shah (skinning) measures to CAT(-1) spaces with potentials. The work presents a proof for the equidistribution of equidistant hypersurfaces to Gibbs measures, and the equidistribution of common perpendicular arcs between, for instance, closed geodesics. Using tools from ergodic theory (including coding by topological Markov shifts, and an appendix by Buzzi that relates weak Gibbs measures and equilibrium states for them), the authors further prove the variational principle and rate of mixing for the geodesic flow on metric and simplicial trees—again without the need for any compactness or torsionfree assumptions. In a series of applications, using the Bruhat-Tits trees over non-Archimedean local fields, the authors subsequently prove further important results: the Mertens formula and the equidistribution of Farey fractions in function fields, the equidistribution of quadratic irrationals over function fields in their completions, and asymptotic counting results of the representations by quadratic norm forms. One of the book's main benefits is that the authors provide explicit error terms throughout. Given its scope, it will be of interest to graduate students and researchers in a wide range of fields, for instance ergodic theory, dynamical systems, geometric group theory, discrete subgroups of locally compact groups, and the arithmetic of function fields.

Equilibrium States And The Ergodic Theory Of Anosov Diffeomorphisms

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Author : Robert Edward Bowen
language : en
Publisher: Springer
Release Date : 2008-04-04

Equilibrium States And The Ergodic Theory Of Anosov Diffeomorphisms written by Robert Edward Bowen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-04 with Mathematics categories.

For this printing of R. Bowen's book, J.-R. Chazottes has retyped it in TeX for easier reading, thereby correcting typos and bibliographic details. From the Preface by D. Ruelle: "Rufus Bowen has left us a masterpiece of mathematical exposition... Here a number of results which were new at the time are presented in such a clear and lucid style that Bowen's monograph immediately became a classic. More than thirty years later, many new results have been proved in this area, but the volume is as useful as ever because it remains the best introduction to the basics of the ergodic theory of hyperbolic systems."

Ergodic Theory And Negative Curvature

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Author : Boris Hasselblatt
language : en
Publisher: Springer
Release Date : 2017-12-15

Ergodic Theory And Negative Curvature written by Boris Hasselblatt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-15 with Mathematics categories.

Focussing on the mathematics related to the recent proof of ergodicity of the (Weil–Petersson) geodesic flow on a nonpositively curved space whose points are negatively curved metrics on surfaces, this book provides a broad introduction to an important current area of research. It offers original textbook-level material suitable for introductory or advanced courses as well as deep insights into the state of the art of the field, making it useful as a reference and for self-study. The first chapters introduce hyperbolic dynamics, ergodic theory and geodesic and horocycle flows, and include an English translation of Hadamard's original proof of the Stable-Manifold Theorem. An outline of the strategy, motivation and context behind the ergodicity proof is followed by a careful exposition of it (using the Hopf argument) and of the pertinent context of Teichmüller theory. Finally, some complementary lectures describe the deep connections between geodesic flows in negative curvature and Diophantine approximation.

Geometry Topology And Dynamics In Negative Curvature

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Author : C. S. Aravinda
language : en
Publisher: Cambridge University Press
Release Date : 2016-01-21

Geometry Topology And Dynamics In Negative Curvature written by C. S. Aravinda and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-21 with Mathematics categories.

Ten high-quality survey articles provide an overview of important recent developments in the mathematics surrounding negative curvature.

Thermodynamic Formalism

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Author : Mark Pollicott
language : en
Publisher: Springer Nature
Release Date : 2021-10-01

Thermodynamic Formalism written by Mark Pollicott and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-01 with Mathematics categories.

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.

Nasa Technical Paper

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Author :
language : en
Publisher:
Release Date : 1989

Nasa Technical Paper written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Astronautics categories.

Certain Problems In The Theory Of Stability Of Motion In The Whole

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Author : V. A. Pliss
language : en
Publisher:
Release Date : 1958

Certain Problems In The Theory Of Stability Of Motion In The Whole written by V. A. Pliss and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1958 with Differential equations categories.

Nasa Technical Translation

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Author :
language : en
Publisher:
Release Date : 1965

Nasa Technical Translation written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1965 with Science categories.

Understanding Acoustics

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Author : Steven L. Garrett
language : en
Publisher: Springer Nature
Release Date : 2020-11-02

Understanding Acoustics written by Steven L. Garrett and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-11-02 with Science categories.

This open access textbook, like Rayleigh’s classic Theory of Sound, focuses on experiments and on approximation techniques rather than mathematical rigor. The second edition has benefited from comments and corrections provided by many acousticians, in particular those who have used the first edition in undergraduate and graduate courses. For example, phasor notation has been added to clearly distinguish complex variables, and there is a new section on radiation from an unbaffled piston. Drawing on over 40 years of teaching experience at UCLA, the Naval Postgraduate School, and Penn State, the author presents a uniform methodology, based on hydrodynamic fundamentals for analysis of lumped-element systems and wave propagation that can accommodate dissipative mechanisms and geometrically-complex media. Five chapters on vibration and elastic waves highlight modern applications, including viscoelasticity and resonance techniques for measurement of elastic moduli, while introducing analytical techniques and approximation strategies that are revisited in nine subsequent chapters describing all aspects of generation, transmission, scattering, and reception of waves in fluids. Problems integrate multiple concepts, and several include experimental data to provide experience in choosing optimal strategies for extraction of experimental results and their uncertainties. Fundamental physical principles that do not ordinarily appear in other acoustics textbooks, like adiabatic invariance, similitude, the Kramers-Kronig relations, and the equipartition theorem, are shown to provide independent tests of results obtained from numerical solutions, commercial software, and simulations. Thanks to the Veneklasen Research Foundation, this popular textbook is now open access, making the e-book available for free download worldwide. Provides graduate-level treatment of acoustics and vibration suitable for use in courses, for self-study, and as a reference Highlights fundamental physical principles that can provide independent tests of the validity of numerical solutions, commercial software, and computer simulations Demonstrates approximation techniques that greatly simplify the mathematics without a substantial decrease in accuracy Incorporates a hydrodynamic approach to the acoustics of sound in fluids that provides a uniform methodology for analysis of lumped-element systems and wave propagation Emphasizes actual applications as examples of topics explained in the text Includes realistic end-of-chapter problems, some including experimental data, as well as a Solutions Manual for instructors. Features “Talk Like an Acoustician“ boxes to highlight key terms introduced in the text.