Ergodic Theory: Independence and Dichotomies: Springer Monographs in Mathematics
Autor David Kerr, Hanfeng Lien Limba Engleză Paperback – 13 iul 2018
The structure of the book is designed to be flexible enough to serve a variety of readers. The discussion of dynamics is developed from scratch assuming some rudimentary functional analysis, measure theory, and topology, and parts of the text can be used as an introductory course. Researchers in ergodic theory and related areas will also find the book valuable as a reference.
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Paperback (1) | 933.27 lei 6-8 săpt. | |
Springer International Publishing – 13 iul 2018 | 933.27 lei 6-8 săpt. | |
Hardback (1) | 818.27 lei 3-5 săpt. | +33.22 lei 7-13 zile |
Springer International Publishing – 27 feb 2017 | 818.27 lei 3-5 săpt. | +33.22 lei 7-13 zile |
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Specificații
ISBN-13: 9783319842547
ISBN-10: 3319842544
Ilustrații: XXXIV, 431 p.
Dimensiuni: 155 x 235 mm
Greutate: 0.65 kg
Ediția:Softcover reprint of the original 1st ed. 2016
Editura: Springer International Publishing
Colecția Springer
Seria Springer Monographs in Mathematics
Locul publicării:Cham, Switzerland
ISBN-10: 3319842544
Ilustrații: XXXIV, 431 p.
Dimensiuni: 155 x 235 mm
Greutate: 0.65 kg
Ediția:Softcover reprint of the original 1st ed. 2016
Editura: Springer International Publishing
Colecția Springer
Seria Springer Monographs in Mathematics
Locul publicării:Cham, Switzerland
Cuprins
Preface.- Introduction.- General Framework and Notational Conventions.- Part 1 Weak Mixing Comactness.- Basic Concepts in Ergodic Theory.- Structure Theory for P.M.P. Actions.- Amenability.- Property (T).- Orbit Equivalence Beyond Amenability.- Topological Dynamics.- Tameness and Independence.- Part 2 Entropy.- Entropy for Actions of Amenable Groups.- Entropy for Actions of Sofic Groups.- The f-invariant.- Entropy and Independence.- Algebraic Actions: Expansiveness, Homoclinicity, and Entropy.- Algebraic Actions: Entropy and the Fuglede-Kadison Determinant.- Appendix A. Polish Spaces and Standard Borel Spaces.- Appendix B. Positive Definite Functions and Weak Containment.- Appendix C. Hilbert Modules.- Appendix D. Weakly Almost Periodic Functions.- Appendix E. Gaussian Actions.
Textul de pe ultima copertă
This book provides an introduction to the ergodic theory and topological dynamics of actions of countable groups. It is organized around the theme of probabilistic and combinatorial independence, and highlights the complementary roles of the asymptotic and the perturbative in its comprehensive treatment of the core concepts of weak mixing, compactness, entropy, and amenability. The more advanced material includes Popa's cocycle superrigidity, the Furstenberg-Zimmer structure theorem, and sofic entropy.
The structure of the book is designed to be flexible enough to serve a variety of readers. The discussion of dynamics is developed from scratch assuming some rudimentary functional analysis, measure theory, and topology, and parts of the text can be used as an introductory course. Researchers in ergodic theory and related areas will also find the book valuable as a reference.
The structure of the book is designed to be flexible enough to serve a variety of readers. The discussion of dynamics is developed from scratch assuming some rudimentary functional analysis, measure theory, and topology, and parts of the text can be used as an introductory course. Researchers in ergodic theory and related areas will also find the book valuable as a reference.
Caracteristici
Provides an introduction to the ergodic theory and topological dynamics of actions of general countable groups Covers several topics of current research interest, including Popa's cocycle superrigidity, sofic entropy, and algebraic actions Contains a consolidated account of amenability and its ramifications for dynamics, including a systematic exposition of the entropy theory for actions of amenable groups Includes supplementary material: sn.pub/extras