Ratner S Theorems On Unipotent Flows
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Ratner S Theorems On Unipotent Flows
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Author : Dave Witte Morris
language : en
Publisher: University of Chicago Press
Release Date : 2005-08-15
Ratner S Theorems On Unipotent Flows written by Dave Witte Morris and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-15 with Mathematics categories.
The theorems of Berkeley mathematician Marina Ratner have guided key advances in the understanding of dynamical systems. Unipotent flows are well-behaved dynamical systems, and Ratner has shown that the closure of every orbit for such a flow is of a simple algebraic or geometric form. In Ratner's Theorems on Unipotent Flows, Dave Witte Morris provides both an elementary introduction to these theorems and an account of the proof of Ratner's measure classification theorem. A collection of lecture notes aimed at graduate students, the first four chapters of Ratner's Theorems on Unipotent Flows can be read independently. The first chapter, intended for a fairly general audience, provides an introduction with examples that illustrate the theorems, some of their applications, and the main ideas involved in the proof. In the following chapters, Morris introduces entropy, ergodic theory, and the theory of algebraic groups. The book concludes with a proof of the measure-theoretic version of Ratner's Theorem. With new material that has never before been published in book form, Ratner's Theorems on Unipotent Flows helps bring these important theorems to a broader mathematical readership.
Ratner S Theorems On Unipotent Flows
DOWNLOAD
Author : Dave Witte Morris
language : en
Publisher: University of Chicago Press
Release Date : 2005-08-15
Ratner S Theorems On Unipotent Flows written by Dave Witte Morris and has been published by University of Chicago Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-08-15 with Mathematics categories.
The theorems of Berkeley mathematician Marina Ratner have guided key advances in the understanding of dynamical systems. Unipotent flows are well-behaved dynamical systems, and Ratner has shown that the closure of every orbit for such a flow is of a simple algebraic or geometric form. In Ratner's Theorems on Unipotent Flows, Dave Witte Morris provides both an elementary introduction to these theorems and an account of the proof of Ratner's measure classification theorem. A collection of lecture notes aimed at graduate students, the first four chapters of Ratner's Theorems on Unipotent Flows can be read independently. The first chapter, intended for a fairly general audience, provides an introduction with examples that illustrate the theorems, some of their applications, and the main ideas involved in the proof. In the following chapters, Morris introduces entropy, ergodic theory, and the theory of algebraic groups. The book concludes with a proof of the measure-theoretic version of Ratner's Theorem. With new material that has never before been published in book form, Ratner's Theorems on Unipotent Flows helps bring these important theorems to a broader mathematical readership.
Handbook Of Dynamical Systems
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Author : B. Hasselblatt
language : en
Publisher: Elsevier
Release Date : 2002-08-20
Handbook Of Dynamical Systems written by B. Hasselblatt and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-08-20 with Mathematics categories.
Volumes 1A and 1B. These volumes give a comprehensive survey of dynamics written by specialists in the various subfields of dynamical systems. The presentation attains coherence through a major introductory survey by the editors that organizes the entire subject, and by ample cross-references between individual surveys. The volumes are a valuable resource for dynamicists seeking to acquaint themselves with other specialties in the field, and to mathematicians active in other branches of mathematics who wish to learn about contemporary ideas and results dynamics. Assuming only general mathematical knowledge the surveys lead the reader towards the current state of research in dynamics. Volume 1B will appear 2005.
Ergodic Theory
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Author : Manfred Einsiedler
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-09-11
Ergodic Theory written by Manfred Einsiedler and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-09-11 with Mathematics categories.
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.
Ergodic Theory And Harmonic Analysis
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Author : Karl E. Petersen
language : en
Publisher: Cambridge University Press
Release Date : 1995-01-27
Ergodic Theory And Harmonic Analysis written by Karl E. Petersen 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 1995-01-27 with Mathematics categories.
Ergodic theory is a field that is stimulating on its own, and also in its interactions with other branches of mathematics and science. In recent years, the interchanges with harmonic analysis have been especially noticeable and productive. This book contains survey papers describing the relationship of ergodic theory with convergence, rigidity theory and the theory of joinings. These papers present the background of each area of interaction, the most outstanding results and promising lines of research. They should form perfect starting points for anyone beginning research in one of these areas. Thirteen related research papers describe the work; several treat questions arising from the Furstenberg multiple recurrence theory, while the remainder deal with convergence and a variety of other topics in dynamics.
Structure And Randomness
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Author : Terence Tao
language : en
Publisher: American Mathematical Soc.
Release Date :
Structure And Randomness written by Terence Tao and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
"In 2007, Terry Tao began a mathematical blog, as an outgrowth of his own website at UCLA. This book is based on a selection of articles from the first year of that blog. These articles discuss a wide range of mathematics and its applications, ranging from expository articles on quantum mechanics, Einstein's equation E = mc[superscript 2], or compressed sensing, to open problems in analysis, combinatorics, geometry, number theory, and algebra, to lecture series on random matrices, Fourier analysis, or the dichotomy between structure and randomness that is present in many subfields of mathematics, to more philosophical discussions on such topics as the interplay between finitary and infinitary in analysis. Some selected commentary from readers of the blog has also been included at the end of each article.
A Vision For Dynamics In The 21st Century
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Author : Danijela Damjanovic
language : en
Publisher: Cambridge University Press
Release Date : 2023-12-31
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 2023-12-31 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.
A Panorama Of Number Theory Or The View From Baker S Garden
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Author : Gisbert Wüstholz
language : en
Publisher: Cambridge University Press
Release Date : 2002-09-26
A Panorama Of Number Theory Or The View From Baker S Garden written by Gisbert Wüstholz 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 2002-09-26 with Mathematics categories.
This is a selection of high quality articles on number theory by leading figures.
I M Gelfand Seminar
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Author : Izrailʹ Moiseevich Gelʹfand
language : en
Publisher: American Mathematical Soc.
Release Date : 1993
I M Gelfand Seminar written by Izrailʹ Moiseevich Gelʹfand and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Funcctional analysis categories.
Equidistribution In Number Theory An Introduction
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Author : Andrew Granville
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-04-08
Equidistribution In Number Theory An Introduction written by Andrew Granville and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-08 with Mathematics categories.
This set of lectures provides a structured introduction to the concept of equidistribution in number theory. This concept is of growing importance in many areas, including cryptography, zeros of L-functions, Heegner points, prime number theory, the theory of quadratic forms, and the arithmetic aspects of quantum chaos. The volume brings together leading researchers from a range of fields who reveal fascinating links between seemingly disparate areas.