Introduction And Cocycle Problem
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Rigidity In Higher Rank Abelian Group Actions Volume 1 Introduction And Cocycle Problem
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Author : Anatole Katok
language : en
Publisher: Cambridge University Press
Release Date : 2011-06-16
Rigidity In Higher Rank Abelian Group Actions Volume 1 Introduction And Cocycle Problem written by Anatole Katok and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-16 with Mathematics categories.
This self-contained monograph presents rigidity theory for a large class of dynamical systems, differentiable higher rank hyperbolic and partially hyperbolic actions. This first volume describes the subject in detail and develops the principal methods presently used in various aspects of the rigidity theory. Part I serves as an exposition and preparation, including a large collection of examples that are difficult to find in the existing literature. Part II focuses on cocycle rigidity, which serves as a model for rigidity phenomena as well as a useful tool for studying them. The book is an ideal reference for applied mathematicians and scientists working in dynamical systems and a useful introduction for graduate students interested in entering the field. Its wealth of examples also makes it excellent supplementary reading for any introductory course in dynamical systems.
Introductory Lectures On Knot Theory
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Author : Louis H. Kauffman
language : en
Publisher: World Scientific
Release Date : 2012
Introductory Lectures On Knot Theory written by Louis H. Kauffman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
More recently, Khovanov introduced link homology as a generalization of the Jones polynomial to homology of chain complexes and Ozsvath and Szabo developed Heegaard-Floer homology, that lifts the Alexander polynomial. These two significantly different theories are closely related and the dependencies are the object of intensive study. These ideas mark the beginning of a new era in knot theory that includes relationships with four-dimensional problems and the creation of new forms of algebraic topology relevant to knot theory. The theory of skein modules is an older development also having its roots in Jones discovery. Another significant and related development is the theory of virtual knots originated independently by Kauffman and by Goussarov Polyak and Viro in the '90s. All these topics and their relationships are the subject of the survey papers in this book.
Probability On Real Lie Algebras
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Author : Uwe Franz
language : en
Publisher: Cambridge University Press
Release Date : 2016-01-25
Probability On Real Lie Algebras written by Uwe Franz and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-25 with Mathematics categories.
This monograph is a progressive introduction to non-commutativity in probability theory, summarizing and synthesizing recent results about classical and quantum stochastic processes on Lie algebras. In the early chapters, focus is placed on concrete examples of the links between algebraic relations and the moments of probability distributions. The subsequent chapters are more advanced and deal with Wigner densities for non-commutative couples of random variables, non-commutative stochastic processes with independent increments (quantum Lévy processes), and the quantum Malliavin calculus. This book will appeal to advanced undergraduate and graduate students interested in the relations between algebra, probability, and quantum theory. It also addresses a more advanced audience by covering other topics related to non-commutativity in stochastic calculus, Lévy processes, and the Malliavin calculus.
Introduction To String Theory
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Author : Sergio Cecotti
language : en
Publisher: Springer Nature
Release Date : 2023-10-06
Introduction To String Theory written by Sergio Cecotti and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-10-06 with Science categories.
Graduate students typically enter into courses on string theory having little to no familiarity with the mathematical background so crucial to the discipline. As such, this book, based on lecture notes, edited and expanded, from the graduate course taught by the author at SISSA and BIMSA, places particular emphasis on said mathematical background. The target audience for the book includes students of both theoretical physics and mathematics. This explains the book’s "strange" style: on the one hand, it is highly didactic and explicit, with a host of examples for the physicists, but, in addition, there are also almost 100 separate technical boxes, appendices, and starred sections, in which matters discussed in the main text are put into a broader mathematical perspective, while deeper and more rigorous points of view (particularly those from the modern era) are presented. The boxes also serve to further shore up the reader’s understanding of the underlying math. In writing this book, the author’s goal was not to achieve any sort of definitive conciseness, opting instead for clarity and "completeness". To this end, several arguments are presented more than once from different viewpoints and in varying contexts.
A Vision For Dynamics In The 21st Century
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Author : Danijela Damjanovic
language : en
Publisher: Cambridge University Press
Release Date : 2024-02-08
A Vision For Dynamics In The 21st Century written by Danijela Damjanovic and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-02-08 with Mathematics categories.
A large international conference celebrated the 50-year career of Anatole Katok and the body of research across smooth dynamics and ergodic theory that he touched. In this book many leading experts provide an account of the latest developments at the research frontier and together set an agenda for future work, including an explicit problem list. This includes elliptic, parabolic, and hyperbolic smooth dynamics, ergodic theory, smooth ergodic theory, and actions of higher-rank groups. The chapters are written in a readable style and give a broad view of each topic; they blend the most current results with the developments leading up to them, and give a perspective on future work. This book is ideal for graduate students, instructors and researchers across all research areas in dynamical systems and related subjects.
The Theory Of Hardy S Z Function
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Author : A. Ivić
language : en
Publisher: Cambridge University Press
Release Date : 2013
The Theory Of Hardy S Z Function written by A. Ivić and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
A comprehensive account of Hardy's Z-function, one of the most important functions of analytic number theory.
Group Cohomology And Algebraic Cycles
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Author : Burt Totaro
language : en
Publisher: Cambridge University Press
Release Date : 2014-06-26
Group Cohomology And Algebraic Cycles written by Burt Totaro and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-06-26 with Mathematics categories.
This book presents a coherent suite of computational tools for the study of group cohomology algebraic cycles.
Descriptive Set Theory And Dynamical Systems
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Author : M. Foreman
language : en
Publisher: Cambridge University Press
Release Date : 2000-05-25
Descriptive Set Theory And Dynamical Systems written by M. Foreman and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-05-25 with Mathematics categories.
In recent years there has been a growing interest in the interactions between descriptive set theory and various aspects of the theory of dynamical systems, including ergodic theory and topological dynamics. This volume, first published in 2000, contains a collection of survey papers by leading researchers covering a wide variety of recent developments in these subjects and their interconnections. This book provides researchers and graduate students interested in either of these areas with a guide to work done in the other, as well as with an introduction to problems and research directions arising from their interconnections.
Index Theory In Nonlinear Analysis
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Author : Chungen Liu
language : en
Publisher: Springer
Release Date : 2019-05-22
Index Theory In Nonlinear Analysis written by Chungen Liu and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-22 with Mathematics categories.
This book provides detailed information on index theories and their applications, especially Maslov-type index theories and their iteration theories for non-periodic solutions of Hamiltonian systems. It focuses on two index theories: L-index theory (index theory for Lagrangian boundary conditions) and P-index theory (index theory for P-boundary conditions). In addition, the book introduces readers to recent advances in the study of index theories for symmetric periodic solutions of nonlinear Hamiltonian systems, and for selected boundary value problems involving partial differential equations.
Defocusing Nonlinear Schr Dinger Equations
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Author : Benjamin Dodson
language : en
Publisher: Cambridge University Press
Release Date : 2019-03-28
Defocusing Nonlinear Schr Dinger Equations written by Benjamin Dodson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-03-28 with Mathematics categories.
Explores Schrödinger equations with power-type nonlinearity, with scattering results for mass- and energy-critical Schrödinger equations.