Thermodynamic Formalism And Applications To Dimension Theory
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Thermodynamic Formalism And Applications To Dimension Theory
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Author :
language : en
Publisher: Springer
Release Date : 2011-08-24
Thermodynamic Formalism And Applications To Dimension Theory written by and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-24 with categories.
Thermodynamic Formalism And Applications To Dimension Theory
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Author : Luis Barreira
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-08-24
Thermodynamic Formalism And Applications To Dimension Theory written by Luis Barreira and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-08-24 with Mathematics categories.
This self-contained monograph presents a unified exposition of the thermodynamic formalism and some of its main extensions, with emphasis on the relation to dimension theory and multifractal analysis of dynamical systems. In particular, the book considers three different flavors of the thermodynamic formalism, namely nonadditive, subadditive, and almost additive, and provides a detailed discussion of some of the most significant results in the area, some of them quite recent. It also includes a discussion of the most substantial applications of these flavors of the thermodynamic formalism to dimension theory and multifractal analysis of dynamical systems.
Dimension Theory Of Hyperbolic Flows
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Author : Luís Barreira
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-12
Dimension Theory Of Hyperbolic Flows written by Luís Barreira and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-12 with Mathematics categories.
The dimension theory of dynamical systems has progressively developed, especially over the last two decades, into an independent and extremely active field of research. Its main aim is to study the complexity of sets and measures that are invariant under the dynamics. In particular, it is essential to characterizing chaotic strange attractors. To date, some parts of the theory have either only been outlined, because they can be reduced to the case of maps, or are too technical for a wider audience. In this respect, the present monograph is intended to provide a comprehensive guide. Moreover, the text is self-contained and with the exception of some basic results in Chapters 3 and 4, all the results in the book include detailed proofs. The book is intended for researchers and graduate students specializing in dynamical systems who wish to have a sufficiently comprehensive view of the theory together with a working knowledge of its main techniques. The discussion of some open problems is also included in the hope that it may lead to further developments. Ideally, readers should have some familiarity with the basic notions and results of ergodic theory and hyperbolic dynamics at the level of an introductory course in the area, though the initial chapters also review all the necessary material.
Equadiff 95 Proceedings Of The International Conference On Differential Equations
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Author : L Magalhaes
language : en
Publisher: World Scientific
Release Date : 1998-04-30
Equadiff 95 Proceedings Of The International Conference On Differential Equations written by L Magalhaes and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998-04-30 with categories.
In this volume, leading experts on differential equations address recent advances in the fields of ordinary differential equations and dynamical systems, partial differential equations and calculus of variations, and their related applications.
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.
Further Developments In Fractals And Related Fields
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Author : Julien Barral
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-02-20
Further Developments In Fractals And Related Fields written by Julien Barral and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-20 with Mathematics categories.
This volume, following in the tradition of a similar 2010 publication by the same editors, is an outgrowth of an international conference, “Fractals and Related Fields II,” held in June 2011. The book provides readers with an overview of developments in the mathematical fields related to fractals, including original research contributions as well as surveys from many of the leading experts on modern fractal theory and applications. The chapters cover fields related to fractals such as: *geometric measure theory *ergodic theory *dynamical systems *harmonic and functional analysis *number theory *probability theory Further Developments in Fractals and Related Fields is aimed at pure and applied mathematicians working in the above-mentioned areas as well as other researchers interested in discovering the fractal domain. Throughout the volume, readers will find interesting and motivating results as well as new avenues for further research.
Mathematics Of Complexity And Dynamical Systems
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Author : Robert A. Meyers
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-10-05
Mathematics Of Complexity And Dynamical Systems written by Robert A. Meyers and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-05 with Mathematics categories.
Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.
Thermodynamic Formalism
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Author : David Ruelle
language : en
Publisher: Cambridge University Press
Release Date : 2004-11-25
Thermodynamic Formalism written by David Ruelle 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 2004-11-25 with Science categories.
Reissued in the Cambridge Mathematical Library this classic book outlines the theory of thermodynamic formalism which was developed to describe the properties of certain physical systems consisting of a large number of subunits. It is aimed at mathematicians interested in ergodic theory, topological dynamics, constructive quantum field theory, the study of certain differentiable dynamical systems, notably Anosov diffeomorphisms and flows. It is also of interest to theoretical physicists concerned with the conceptual basis of equilibrium statistical mechanics. The level of the presentation is generally advanced, the objective being to provide an efficient research tool and a text for use in graduate teaching. Background material on mathematics has been collected in appendices to help the reader. Extra material is given in the form of updates of problems that were open at the original time of writing and as a new preface specially written for this new edition by the author.
Geometry And Analysis Of Fractals
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Author : De-Jun Feng
language : en
Publisher: Springer
Release Date : 2014-08-01
Geometry And Analysis Of Fractals written by De-Jun Feng and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-01 with Mathematics categories.
This volume collects thirteen expository or survey articles on topics including Fractal Geometry, Analysis of Fractals, Multifractal Analysis, Ergodic Theory and Dynamical Systems, Probability and Stochastic Analysis, written by the leading experts in their respective fields. The articles are based on papers presented at the International Conference on Advances on Fractals and Related Topics, held on December 10-14, 2012 at the Chinese University of Hong Kong. The volume offers insights into a number of exciting, cutting-edge developments in the area of fractals, which has close ties to and applications in other areas such as analysis, geometry, number theory, probability and mathematical physics.
A Non Additive Thermodynamic Formalism And Applications To The Dimension Theory Of Hyperbolic Dynamics
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Author : Luis Barreira
language : en
Publisher:
Release Date : 1995
A Non Additive Thermodynamic Formalism And Applications To The Dimension Theory Of Hyperbolic Dynamics written by Luis Barreira and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with categories.