Thermodynamic Formalism And Holomorphic Dynamical Systems
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Thermodynamic Formalism And Holomorphic Dynamical Systems
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Author : Michel Zinsmeister
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Thermodynamic Formalism And Holomorphic Dynamical Systems written by Michel Zinsmeister and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Thermodynamics helps in understanding the equilibrium of a gas or the different states of matter, and recently it has also become a powerful tool for understanding the objects of holomorphic dynamical systems. While the reasons remain obscure, this book begins to describe the physical and mathematical aspects of this relationship in order to understand how it works and how useful it can be. Annotation copyrighted by Book News, Inc., Portland, OR
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.
Analytic Endomorphisms Of The Riemann Sphere
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Author : Mariusz Urbański
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2023-09-05
Analytic Endomorphisms Of The Riemann Sphere written by Mariusz Urbański and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-09-05 with Mathematics categories.
Complex dynamics is one of the most fascinating subjects of study and research in mathematics. This third volume in the series entitled Non-Invertible Dynamical Systems not only examines topological and analytical properties of the iteration of rational functions on the Riemann sphere (in particular, the Fatou and Julia sets) but also focuses on thermodynamic, ergodic and fractal properties of these functions (notably, equilibrium states, Bowen's formula and Sullivan’s conformal measures). This volume builds on the first two volumes in the series while simultaneously developing some methods and techniques specific to rational functions.
Open Conformal Systems And Perturbations Of Transfer Operators
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Author : Mark Pollicott
language : en
Publisher: Springer
Release Date : 2018-02-05
Open Conformal Systems And Perturbations Of Transfer Operators written by Mark Pollicott and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-02-05 with Mathematics categories.
The focus of this book is on open conformal dynamical systems corresponding to the escape of a point through an open Euclidean ball. The ultimate goal is to understand the asymptotic behavior of the escape rate as the radius of the ball tends to zero. In the case of hyperbolic conformal systems this has been addressed by various authors. The conformal maps considered in this book are far more general, and the analysis correspondingly more involved. The asymptotic existence of escape rates is proved and they are calculated in the context of (finite or infinite) countable alphabets, uniformly contracting conformal graph-directed Markov systems, and in particular, conformal countable alphabet iterated function systems. These results have direct applications to interval maps, rational functions and meromorphic maps. Towards this goal the authors develop, on a purely symbolic level, a theory of singular perturbations of Perron--Frobenius (transfer) operators associated with countable alphabet subshifts of finite type and Hölder continuous summable potentials. This leads to a fairly full account of the structure of the corresponding open dynamical systems and their associated surviving sets.
Ergodic Theory Finite And Infinite Thermodynamic Formalism Symbolic Dynamics And Distance Expanding Maps
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Author : Mariusz Urbański
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2021-11-22
Ergodic Theory Finite And Infinite Thermodynamic Formalism Symbolic Dynamics And Distance Expanding Maps written by Mariusz Urbański and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-11-22 with Mathematics categories.
The book contains a detailed treatment of thermodynamic formalism on general compact metrizable spaces. Topological pressure, topological entropy, variational principle, and equilibrium states are presented in detail. Abstract ergodic theory is also given a significant attention. Ergodic theorems, ergodicity, and Kolmogorov-Sinai metric entropy are fully explored. Furthermore, the book gives the reader an opportunity to find rigorous presentation of thermodynamic formalism for distance expanding maps and, in particular, subshifts of finite type over a finite alphabet. It also provides a fairly complete treatment of subshifts of finite type over a countable alphabet. Transfer operators, Gibbs states and equilibrium states are, in this context, introduced and dealt with. Their relations are explored. All of this is applied to fractal geometry centered around various versions of Bowen’s formula in the context of expanding conformal repellors, limit sets of conformal iterated function systems and conformal graph directed Markov systems. A unique introduction to iteration of rational functions is given with emphasize on various phenomena caused by rationally indifferent periodic points. Also, a fairly full account of the classicaltheory of Shub’s expanding endomorphisms is given; it does not have a book presentation in English language mathematical literature.
Ergodic Theory
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Author : Cesar E. Silva
language : en
Publisher: Springer Nature
Release Date : 2023-07-31
Ergodic Theory written by Cesar E. Silva and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-07-31 with Mathematics categories.
This volume in the Encyclopedia of Complexity and Systems Science, Second Edition, covers recent developments in classical areas of ergodic theory, including the asymptotic properties of measurable dynamical systems, spectral theory, entropy, ergodic theorems, joinings, isomorphism theory, recurrence, nonsingular systems. It enlightens connections of ergodic theory with symbolic dynamics, topological dynamics, smooth dynamics, combinatorics, number theory, pressure and equilibrium states, fractal geometry, chaos. In addition, the new edition includes dynamical systems of probabilistic origin, ergodic aspects of Sarnak's conjecture, translation flows on translation surfaces, complexity and classification of measurable systems, operator approach to asymptotic properties, interplay with operator algebras
Holomorphic Dynamical Systems
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Author : Nessim Sibony
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-07-31
Holomorphic Dynamical Systems written by Nessim Sibony 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 2010-07-31 with Mathematics categories.
The theory of holomorphic dynamical systems is a subject of increasing interest in mathematics, both for its challenging problems and for its connections with other branches of pure and applied mathematics. A holomorphic dynamical system is the datum of a complex variety and a holomorphic object (such as a self-map or a vector ?eld) acting on it. The study of a holomorphic dynamical system consists in describing the asymptotic behavior of the system, associating it with some invariant objects (easy to compute) which describe the dynamics and classify the possible holomorphic dynamical systems supported by a given manifold. The behavior of a holomorphic dynamical system is pretty much related to the geometry of the ambient manifold (for instance, - perbolic manifolds do no admit chaotic behavior, while projective manifolds have a variety of different chaotic pictures). The techniques used to tackle such pr- lems are of variouskinds: complexanalysis, methodsof real analysis, pluripotential theory, algebraic geometry, differential geometry, topology. To cover all the possible points of view of the subject in a unique occasion has become almost impossible, and the CIME session in Cetraro on Holomorphic Dynamical Systems was not an exception.
Hamiltonian Systems And Their Integrability
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Author : Mich'le Audin
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Hamiltonian Systems And Their Integrability written by Mich'le Audin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
Hamiltonian systems began as a mathematical approach to the study of mechanical systems. As the theory developed, it became clear that the systems that had a sufficient number of conserved quantities enjoyed certain remarkable properties. These are the completely integrable systems. In time, a rich interplay arose between integrable systems and other areas of mathematics, particularly topology, geometry, and group theory.This book presents some modern techniques in the theory of integrable systems viewed as variations on the theme of action-angle coordinates. These techniques include analytical methods coming from the Galois theory of differential equations, as well as more classical algebro-geometric methods related to Lax equations. Audin has included many examples and exercises. Most of the exercises build on the material in the text. None of the important proofs have been relegated to the exercises. Many of the examples are classical, rather than abstract. This book would be suitable for a graduate course in Hamiltonian systems.
Complex Dynamics And Geometry
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Author : Dominique Cerveau
language : en
Publisher: American Mathematical Soc.
Release Date : 2003
Complex Dynamics And Geometry written by Dominique Cerveau and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
In the last twenty years, the theory of holomorphic dynamical systems has had a resurgence of activity, particularly concerning the fine analysis of Julia sets associated with polynomials and rational maps in one complex variable. At the same time, closely related theories have had a similar rapid development, for example the qualitative theory of differential equations in the complex domain. The meeting, ``Etat de la recherche'', held at Ecole Normale Superieure de Lyon, presented the current state of the art in this area, emphasizing the unity linking the various sub-domains. This volume contains four survey articles corresponding to the talks presented at this meeting. D. Cerveau describes the structure of polynomial differential equations in the complex plane, focusing on the local analysis in neighborhoods of singular points. E. Ghys surveys the theory of laminations by Riemann surfaces which occur in many dynamical or geometrical situations. N. Sibony describes the present state of the generalization of the Fatou-Julia theory for polynomial or rational maps in two or more complex dimensions. Lastly, the talk by J.-C. Yoccoz, written by M. Flexor, considers polynomials of degree $2$ in one complex variable, and in particular, with the hyperbolic properties of these polynomials centered around the Jakobson theorem. This is a general introduction that gives a basic history of holomorphic dynamical systems, demonstrating the numerous and fruitful interactions among the topics. In the spirit of the ``Etat de la recherche de la SMF'' meetings, the articles are written for a broad mathematical audience, especially students or mathematicians working in different fields. This book is translated from the French edition by Leslie Kay.
The Schur Algorithm Reproducing Kernel Spaces And System Theory
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Author : Daniel Alpay
language : en
Publisher: American Mathematical Soc.
Release Date : 2001
The Schur Algorithm Reproducing Kernel Spaces And System Theory written by Daniel Alpay and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Computers categories.
Looks at matrix-valued Schur functions and their applications from the unifying point of view of space with reproducing kernels to study the relationship between the modeling of time-invariant dissipative linear systems and the theory of linear operators. Chapters cover reproducing kernel spaces, theory of linear systems, the Schur algorithm and the inverse scattering problem, operator models, interpolation, the indefinite case, the non-stationary case, and Riemann surfaces. Originally published in French by Societe Mathematique de France, 1998. Translated from the French by Stephen S. Wilson. Author information is not given. c. Book News Inc.