Ergodic Theory - Introductory Lectures
Author | : P. Walters |
Publisher | : |
Total Pages | : 212 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9783662166673 |
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Author | : P. Walters |
Publisher | : |
Total Pages | : 212 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9783662166673 |
Author | : Peter Walters |
Publisher | : |
Total Pages | : 372 |
Release | : 1975 |
Genre | : Differential equations, Partial |
ISBN | : 9780387071633 |
Author | : P. Walters |
Publisher | : Springer |
Total Pages | : 209 |
Release | : 2007-12-03 |
Genre | : Mathematics |
ISBN | : 3540374949 |
Author | : Peter Walters |
Publisher | : Springer Science & Business Media |
Total Pages | : 268 |
Release | : 2000-10-06 |
Genre | : Mathematics |
ISBN | : 9780387951522 |
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 | : Peter Walters |
Publisher | : |
Total Pages | : 0 |
Release | : 1999 |
Genre | : Ergodic theory |
ISBN | : |
Author | : Paul R. Halmos |
Publisher | : Courier Dover Publications |
Total Pages | : 113 |
Release | : 2017-12-13 |
Genre | : Mathematics |
ISBN | : 0486814890 |
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 | : Paul R. Halmos |
Publisher | : Courier Dover Publications |
Total Pages | : 113 |
Release | : 2017-11-15 |
Genre | : Mathematics |
ISBN | : 0486826848 |
This concise classic by a well-known master of mathematical exposition covers recurrence, ergodic theorems, ergodicity and mixing properties, and the relation between conjugacy and equivalence. 1956 edition.
Author | : Mark Pollicott |
Publisher | : Cambridge University Press |
Total Pages | : 176 |
Release | : 1993-02-04 |
Genre | : Mathematics |
ISBN | : 9780521435932 |
These lecture notes provide a unique introduction to Pesin theory and its applications.
Author | : Manfred Einsiedler |
Publisher | : Springer Science & Business Media |
Total Pages | : 486 |
Release | : 2010-09-11 |
Genre | : Mathematics |
ISBN | : 0857290215 |
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 | : Karl E. Petersen |
Publisher | : Cambridge University Press |
Total Pages | : 348 |
Release | : 1989-11-23 |
Genre | : Mathematics |
ISBN | : 9780521389976 |
The study of dynamical systems forms a vast and rapidly developing field even when one considers only activity whose methods derive mainly from measure theory and functional analysis. Karl Petersen has written a book which presents the fundamentals of the ergodic theory of point transformations and then several advanced topics which are currently undergoing intense research. By selecting one or more of these topics to focus on, the reader can quickly approach the specialized literature and indeed the frontier of the area of interest. Each of the four basic aspects of ergodic theory - examples, convergence theorems, recurrence properties, and entropy - receives first a basic and then a more advanced, particularized treatment. At the introductory level, the book provides clear and complete discussions of the standard examples, the mean and pointwise ergodic theorems, recurrence, ergodicity, weak mixing, strong mixing, and the fundamentals of entropy. Among the advanced topics are a thorough treatment of maximal functions and their usefulness in ergodic theory, analysis, and probability, an introduction to almost-periodic functions and topological dynamics, a proof of the Jewett-Krieger Theorem, an introduction to multiple recurrence and the Szemeredi-Furstenberg Theorem, and the Keane-Smorodinsky proof of Ornstein's Isomorphism Theorem for Bernoulli shifts. The author's easily-readable style combined with the profusion of exercises and references, summaries, historical remarks, and heuristic discussions make this book useful either as a text for graduate students or self-study, or as a reference work for the initiated.