An Introduction To Ergodic Theory PDF Download
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| Author | : Peter Walters |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 268 |
| Release | : 2000-10-06 |
| Genre | : Mathematics |
| ISBN | : 9780387951522 |
Download An Introduction to Ergodic Theory Book in PDF, ePub and Kindle
The first part of this introduction to ergodic theory addresses measure-preserving transformations of probability spaces and covers such topics as recurrence properties and the Birkhoff ergodic theorem. The second part focuses on the ergodic theory of continuous transformations of compact metrizable spaces. Several examples are detailed, and the final chapter outlines results and applications of ergodic theory to other branches of mathematics.
| Author | : Manfred Einsiedler |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 486 |
| Release | : 2010-09-11 |
| Genre | : Mathematics |
| ISBN | : 0857290215 |
Download Ergodic Theory Book in PDF, ePub and Kindle
This text is a rigorous introduction to ergodic theory, developing the machinery of conditional measures and expectations, mixing, and recurrence. Beginning by developing the basics of ergodic theory and progressing to describe some recent applications to number theory, this book goes beyond the standard texts in this topic. Applications include Weyl's polynomial equidistribution theorem, the ergodic proof of Szemeredi's theorem, the connection between the continued fraction map and the modular surface, and a proof of the equidistribution of horocycle orbits. Ergodic Theory with a view towards Number Theory will appeal to mathematicians with some standard background in measure theory and functional analysis. No background in ergodic theory or Lie theory is assumed, and a number of exercises and hints to problems are included, making this the perfect companion for graduate students and researchers in ergodic theory, homogenous dynamics or number theory.
| Author | : Jon Aaronson |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 298 |
| Release | : 1997 |
| Genre | : Mathematics |
| ISBN | : 0821804944 |
Download An Introduction to Infinite Ergodic Theory Book in PDF, ePub and Kindle
Infinite ergodic theory is the study of measure preserving transformations of infinite measure spaces. The book focuses on properties specific to infinite measure preserving transformations. The work begins with an introduction to basic nonsingular ergodic theory, including recurrence behaviour, existence of invariant measures, ergodic theorems, and spectral theory. A wide range of possible "ergodic behaviour" is catalogued in the third chapter mainly according to the yardsticks of intrinsic normalizing constants, laws of large numbers, and return sequences. The rest of the book consists of illustrations of these phenomena, including Markov maps, inner functions, and cocycles and skew products. One chapter presents a start on the classification theory.
| Author | : P. Walters |
| Publisher | : Springer |
| Total Pages | : 209 |
| Release | : 2007-12-03 |
| Genre | : Mathematics |
| ISBN | : 3540374949 |
Download Ergodic Theory — Introductory Lectures Book in PDF, ePub and Kindle
| Author | : César Ernesto Silva |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 274 |
| Release | : 2008 |
| Genre | : Ergodic theory |
| ISBN | : 0821844202 |
Download Invitation to Ergodic Theory Book in PDF, ePub and Kindle
"Several examples of a dynamical system are developed in detail to illustrate various dynamical concepts. These include in particular the baker's transformation, irrational rotations, the dyadic odometer, the Hajian-Kakutani transformation, the Gauss transformation, and the Chacon transformation. There is a detailed discussion of cutting and stacking transformations in ergodic theory. The book includes several exercises and some open questions to give the flavor of current research. The book also introduces some notions from topological dynamics, such as minimality, transitivity and symbolic spaces; and develops some metric topology, including the Baire category theorem."--BOOK JACKET.
| Author | : Paul R. Halmos |
| Publisher | : Courier Dover Publications |
| Total Pages | : 113 |
| Release | : 2017-12-13 |
| Genre | : Mathematics |
| ISBN | : 0486814890 |
Download Lectures on Ergodic Theory Book in PDF, ePub and Kindle
This concise classic by Paul R. Halmos, a well-known master of mathematical exposition, has served as a basic introduction to aspects of ergodic theory since its first publication in 1956. "The book is written in the pleasant, relaxed, and clear style usually associated with the author," noted the Bulletin of the American Mathematical Society, adding, "The material is organized very well and painlessly presented." Suitable for advanced undergraduates and graduate students in mathematics, the treatment covers recurrence, mean and pointwise convergence, ergodic theorem, measure algebras, and automorphisms of compact groups. Additional topics include weak topology and approximation, uniform topology and approximation, invariant measures, unsolved problems, and other subjects.
| Author | : Yves Coudène |
| Publisher | : Springer |
| Total Pages | : 192 |
| Release | : 2016-11-10 |
| Genre | : Mathematics |
| ISBN | : 1447172876 |
Download Ergodic Theory and Dynamical Systems Book in PDF, ePub and Kindle
This textbook is a self-contained and easy-to-read introduction to ergodic theory and the theory of dynamical systems, with a particular emphasis on chaotic dynamics. This book contains a broad selection of topics and explores the fundamental ideas of the subject. Starting with basic notions such as ergodicity, mixing, and isomorphisms of dynamical systems, the book then focuses on several chaotic transformations with hyperbolic dynamics, before moving on to topics such as entropy, information theory, ergodic decomposition and measurable partitions. Detailed explanations are accompanied by numerous examples, including interval maps, Bernoulli shifts, toral endomorphisms, geodesic flow on negatively curved manifolds, Morse-Smale systems, rational maps on the Riemann sphere and strange attractors. Ergodic Theory and Dynamical Systems will appeal to graduate students as well as researchers looking for an introduction to the subject. While gentle on the beginning student, the book also contains a number of comments for the more advanced reader.
| Author | : Karma Dajani |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 190 |
| Release | : 2002-12-31 |
| Genre | : Mathematics |
| ISBN | : 0883850346 |
Download Ergodic Theory of Numbers Book in PDF, ePub and Kindle
Ergodic Theory of Numbers looks at the interaction between two fields of mathematics: number theory and ergodic theory (as part of dynamical systems). It is an introduction to the ergodic theory behind common number expansions, like decimal expansions, continued fractions, and many others. However, its aim does not stop there. For undergraduate students with sufficient background knowledge in real analysis and graduate students interested in the area, it is also an introduction to a "dynamical way of thinking". The questions studied here are dynamical as well as number theoretical in nature, and the answers are obtained with the help of ergodic theory. Attention is focused on concepts like measure-preserving, ergodicity, natural extension, induced transformations, and entropy. These concepts are then applied to familiar expansions to obtain old and new results in an elegant and straightforward manner. What it means to be ergodic and the basic ideas behind ergodic theory will be explained along the way. The subjects covered vary from classical to recent, which makes this book appealing to researchers as well as students.
| Author | : Ricardo Mañé |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 317 |
| Release | : 1987-01 |
| Genre | : Entropia |
| ISBN | : 9783540152781 |
Download Ergodic Theory and Differentiable Dynamics Book in PDF, ePub and Kindle
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 | : I. P. Cornfeld |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 487 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 1461569273 |
Download Ergodic Theory Book in PDF, ePub and Kindle
Ergodic theory is one of the few branches of mathematics which has changed radically during the last two decades. Before this period, with a small number of exceptions, ergodic theory dealt primarily with averaging problems and general qualitative questions, while now it is a powerful amalgam of methods used for the analysis of statistical properties of dyna mical systems. For this reason, the problems of ergodic theory now interest not only the mathematician, but also the research worker in physics, biology, chemistry, etc. The outline of this book became clear to us nearly ten years ago but, for various reasons, its writing demanded a long period of time. The main principle, which we adhered to from the beginning, was to develop the approaches and methods or ergodic theory in the study of numerous concrete examples. Because of this, Part I of the book contains the description of various classes of dynamical systems, and their elementary analysis on the basis of the fundamental notions of ergodicity, mixing, and spectra of dynamical systems. Here, as in many other cases, the adjective" elementary" i~ not synonymous with "simple. " Part II is devoted to "abstract ergodic theory. " It includes the construc tion of direct and skew products of dynamical systems, the Rohlin-Halmos lemma, and the theory of special representations of dynamical systems with continuous time. A considerable part deals with entropy.
