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Author : Mariusz Urbański
Publisher : de Gruyter
Page : 0 pages
File Size : 24,93 MB
Release : 2022
Category : Mathematics
ISBN : 9783110702644
The book contains detailed treatment of thermodynamic formalism. Topological pressure, entropy, variational principle, and equilibrium states are presented in detail in the first volume. Abstract ergodic theory is also given a significant attention.
Author : Mariusz Urbański
Publisher :
Page : 0 pages
File Size : 39,2 MB
Release : 2022
Category : Dynamics
ISBN :
"This book consists of three volumes. The first volume contains introductory accounts of topological dynamical systems, fi nite-state symbolic dynamics, distance expanding maps, and ergodic theory of metric dynamical systems acting on probability measure spaces, including metric entropy theory of Kolmogorov and Sinai. More advanced topics comprise infi nite ergodic theory, general thermodynamic formalism, topological entropy and pressure. Thermodynamic formalism of distance expanding maps and countable-alphabet subshifts of fi nite type, graph directed Markov systems, conformal expanding repellers, and Lasota-Yorke maps are treated in the second volume, which also contains a chapter on fractal geometry and its applications to conformal systems. Multifractal analysis and real analyticity of pressure are also covered. The third volume is devoted to the study of dynamics, ergodic theory, thermodynamic formalism and fractal geometry of rational functions of the Riemann sphere." --Provided by publisher.
Author : Mariusz Urbański
Publisher : Walter de Gruyter GmbH & Co KG
Page : 458 pages
File Size : 32,16 MB
Release : 2021-11-22
Category : Mathematics
ISBN : 3110702681
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.
Author : Mariusz Urbański
Publisher : Walter de Gruyter GmbH & Co KG
Page : 524 pages
File Size : 25,24 MB
Release : 2022-05-23
Category : Mathematics
ISBN : 311070269X
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.
Author : Luís Barreira
Publisher : Springer Science & Business Media
Page : 295 pages
File Size : 41,44 MB
Release : 2012-04-28
Category : Mathematics
ISBN : 3642280900
Over the last two decades, the dimension theory of dynamical systems has progressively developed into an independent and extremely active field of research. The main aim of this volume is to offer a unified, self-contained introduction to the interplay of these three main areas of research: ergodic theory, hyperbolic dynamics, and dimension theory. It starts with the basic notions of the first two topics and ends with a sufficiently high-level introduction to the third. Furthermore, it includes an introduction to the thermodynamic formalism, which is an important tool in dimension theory. The volume is primarily intended for graduate students interested in dynamical systems, as well as researchers in other areas who wish to learn about ergodic theory, thermodynamic formalism, or dimension theory of hyperbolic dynamics at an intermediate level in a sufficiently detailed manner. In particular, it can be used as a basis for graduate courses on any of these three subjects. The text can also be used for self-study: it is self-contained, and with the exception of some well-known basic facts from other areas, all statements include detailed proofs.
Author : Luis Barreira
Publisher : Springer Science & Business Media
Page : 300 pages
File Size : 44,29 MB
Release : 2011-08-24
Category : Mathematics
ISBN : 3034802064
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.
Author : Mariusz Mario Sara Urbański Roy Munday
Publisher : de Gruyter
Page : 0 pages
File Size : 38,15 MB
Release : 2022-05-23
Category : Dynamics
ISBN : 9783110700619
The book contains detailed treatment of thermodynamic formalism. Distance expanding maps and Lasota-Yorke maps of an interval are then treated in the second volume, which also contains a chapter on fractal geometry and its applications to conformal
Author : Ricardo Mane
Publisher : Springer Science & Business Media
Page : 328 pages
File Size : 20,2 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 3642703356
This version differs from the Portuguese edition only in a few additions and many minor corrections. Naturally, this edition raised the question of whether to use the opportunity to introduce major additions. In a book like this, ending in the heart of a rich research field, there are always further topics that should arguably be included. Subjects like geodesic flows or the role of Hausdorff dimension in con temporary ergodic theory are two of the most tempting gaps to fill. However, I let it stand with practically the same boundaries as the original version, still believing these adequately fulfill its goal of presenting the basic knowledge required to approach the research area of Differentiable Ergodic Theory. I wish to thank Dr. Levy for the excellent translation and several of the correc tions mentioned above. Rio de Janeiro, January 1987 Ricardo Mane Introduction This book is an introduction to ergodic theory, with emphasis on its relationship with the theory of differentiable dynamical systems, which is sometimes called differentiable ergodic theory. Chapter 0, a quick review of measure theory, is included as a reference. Proofs are omitted, except for some results on derivatives with respect to sequences of partitions, which are not generally found in standard texts on measure and integration theory and tend to be lost within a much wider framework in more advanced texts.
Author : Ali Baklouti
Publisher : Walter de Gruyter GmbH & Co KG
Page : 498 pages
File Size : 49,76 MB
Release : 2022-07-05
Category : Mathematics
ISBN : 3110765306
This book contains the latest developments of the theory of discontinuous groups acting on homogenous spaces, from basic concepts to a comprehensive exposition. It develops the newest approaches and methods in the deformation theory of topological modules and unitary representations and focuses on the geometry of discontinuous groups of solvable Lie groups and their compact extensions. It also presents proofs of recent results, computes fundamental examples, and serves as an introduction and reference for students and experienced researchers in Lie theory, discontinuous groups, and deformation (and moduli) spaces.
Author : Friedrich Haslinger
Publisher : Walter de Gruyter GmbH & Co KG
Page : 336 pages
File Size : 46,88 MB
Release : 2023-09-18
Category : Mathematics
ISBN : 3111182924
This book's subject lies in the nexus of partial differential equations, operator theory, and complex analysis. The spectral analysis of the complex Laplacian and the compactness of the d-bar-Neumann operator are primary topics.The revised 2nd edition explores updates to Schrödinger operators with magnetic fields and connections to the Segal Bargmann space (Fock space), to quantum mechanics, and the uncertainty principle.