Recurrence in Ergodic Theory and Combinatorial Number Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Recurrence in Ergodic Theory and Combinatorial Number Theory write by Harry Furstenberg. This book was released on 2014-07-14. Recurrence in Ergodic Theory and Combinatorial Number Theory available in PDF, EPUB and Kindle. Topological dynamics and ergodic theory usually have been treated independently. H. Furstenberg, instead, develops the common ground between them by applying the modern theory of dynamical systems to combinatories and number theory. Originally published in 1981. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Ergodic Theory
Ergodic Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Ergodic Theory write by Manfred Einsiedler. This book was released on 2010-09-11. Ergodic Theory available 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.
Recurrence in Topological Dynamics
Recurrence in Topological Dynamics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Recurrence in Topological Dynamics write by Ethan Akin. This book was released on 1997-07-31. Recurrence in Topological Dynamics available in PDF, EPUB and Kindle. This groundbreaking volume is the first to elaborate the theory of set families as a tool for studying the phenomenon of recurrence. The theory is implicit in such seminal works as Hillel Furstenberg's Recurrence in Ergodic Theory and Combinational Number Theory, but Ethan Akin's study elaborates it in detail, defining such elements of theory as: open families of special subsets the unification of several ideas associated with transitivity, ergodicity, and mixing the Ellis theory of enveloping semigroups for compact dynamical systems and new notions of equicontinuity, distality, and rigidity.
Operator Theoretic Aspects of Ergodic Theory
Operator Theoretic Aspects of Ergodic Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Operator Theoretic Aspects of Ergodic Theory write by Tanja Eisner. This book was released on 2015-11-18. Operator Theoretic Aspects of Ergodic Theory available in PDF, EPUB and Kindle. Stunning recent results by Host–Kra, Green–Tao, and others, highlight the timeliness of this systematic introduction to classical ergodic theory using the tools of operator theory. Assuming no prior exposure to ergodic theory, this book provides a modern foundation for introductory courses on ergodic theory, especially for students or researchers with an interest in functional analysis. While basic analytic notions and results are reviewed in several appendices, more advanced operator theoretic topics are developed in detail, even beyond their immediate connection with ergodic theory. As a consequence, the book is also suitable for advanced or special-topic courses on functional analysis with applications to ergodic theory. Topics include: • an intuitive introduction to ergodic theory • an introduction to the basic notions, constructions, and standard examples of topological dynamical systems • Koopman operators, Banach lattices, lattice and algebra homomorphisms, and the Gelfand–Naimark theorem • measure-preserving dynamical systems • von Neumann’s Mean Ergodic Theorem and Birkhoff’s Pointwise Ergodic Theorem • strongly and weakly mixing systems • an examination of notions of isomorphism for measure-preserving systems • Markov operators, and the related concept of a factor of a measure preserving system • compact groups and semigroups, and a powerful tool in their study, the Jacobs–de Leeuw–Glicksberg decomposition • an introduction to the spectral theory of dynamical systems, the theorems of Furstenberg and Weiss on multiple recurrence, and applications of dynamical systems to combinatorics (theorems of van der Waerden, Gallai,and Hindman, Furstenberg’s Correspondence Principle, theorems of Roth and Furstenberg–Sárközy) Beyond its use in the classroom, Operator Theoretic Aspects of Ergodic Theory can serve as a valuable foundation for doing research at the intersection of ergodic theory and operator theory
Mathematics of Ramsey Theory
Mathematics of Ramsey Theory - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Mathematics of Ramsey Theory write by Jaroslav Nesetril. This book was released on 2012-12-06. Mathematics of Ramsey Theory available in PDF, EPUB and Kindle. One of the important areas of contemporary combinatorics is Ramsey theory. Ramsey theory is basically the study of structure preserved under partitions. The general philosophy is reflected by its interdisciplinary character. The ideas of Ramsey theory are shared by logicians, set theorists and combinatorists, and have been successfully applied in other branches of mathematics. The whole subject is quickly developing and has some new and unexpected applications in areas as remote as functional analysis and theoretical computer science. This book is a homogeneous collection of research and survey articles by leading specialists. It surveys recent activity in this diverse subject and brings the reader up to the boundary of present knowledge. It covers virtually all main approaches to the subject and suggests various problems for individual research.
