Ratner S Theorems On Unipotent Flows

Author : Dave Witte Morris
Publisher : University of Chicago Press
Page : 216 pages
File Size : 40,8 Mb
Release : 2005-08-15
Category : Mathematics
ISBN : 9780226539843

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Ratner's Theorems on Unipotent Flows by Dave Witte Morris Pdf

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.

Author : Dave Witte Morris
Publisher : University of Chicago Press
Page : 224 pages
File Size : 46,5 Mb
Release : 2005-08-15
Category : Mathematics
ISBN : 0226539830

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Ratner's Theorems on Unipotent Flows by Dave Witte Morris Pdf

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.

Author : B. Hasselblatt,A. Katok
Publisher : Elsevier
Page : 1232 pages
File Size : 44,8 Mb
Release : 2002-08-20
Category : Mathematics
ISBN : 9780080533445

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Handbook of Dynamical Systems by B. Hasselblatt,A. Katok Pdf

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.

Author : Manfred Einsiedler,Thomas Ward
Publisher : Springer Science & Business Media
Page : 481 pages
File Size : 50,7 Mb
Release : 2010-09-11
Category : Mathematics
ISBN : 9780857290212

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Ergodic Theory by Manfred Einsiedler,Thomas Ward Pdf

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
Page : 452 pages
File Size : 48,7 Mb
Release : 1995-01-27
Category : Mathematics
ISBN : 9780521459990

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Ergodic Theory and Harmonic Analysis by Karl E. Petersen Pdf

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.

Author : Terence Tao
Publisher : American Mathematical Soc.
Page : 316 pages
File Size : 44,9 Mb
Release : 2024-05-06
Category : Mathematics
ISBN : 0821886282

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Structure and Randomness by Terence Tao Pdf

"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.

Author : Danijela Damjanovic,Boris Hasselblatt,Andrey Gogolev,Yakov Pesin
Publisher : Cambridge University Press
Page : 446 pages
File Size : 47,5 Mb
Release : 2023-12-31
Category : Mathematics
ISBN : 9781009278874

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A Vision for Dynamics in the 21st Century by Danijela Damjanovic,Boris Hasselblatt,Andrey Gogolev,Yakov Pesin Pdf

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.

Author : Gisbert Wüstholz
Publisher : Cambridge University Press
Page : 378 pages
File Size : 49,9 Mb
Release : 2002-09-26
Category : Mathematics
ISBN : 0521807999

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A Panorama of Number Theory Or The View from Baker's Garden by Gisbert Wüstholz Pdf

This is a selection of high quality articles on number theory by leading figures.

Author : Izrailʹ Moiseevich Gelʹfand
Publisher : American Mathematical Soc.
Page : 264 pages
File Size : 48,9 Mb
Release : 1993
Category : Funcctional analysis
ISBN : 0821841181

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I. M. Gelfand Seminar by Izrailʹ Moiseevich Gelʹfand Pdf

Author : Andrew Granville,Zeév Rudnick
Publisher : Springer Science & Business Media
Page : 356 pages
File Size : 51,5 Mb
Release : 2007-04-08
Category : Mathematics
ISBN : 9781402054044

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Equidistribution in Number Theory, An Introduction by Andrew Granville,Zeév Rudnick Pdf

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.

Author : D.V. Anosov
Publisher : Springer Science & Business Media
Page : 242 pages
File Size : 47,6 Mb
Release : 2013-03-14
Category : Mathematics
ISBN : 9783662031728

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Dynamical Systems IX by D.V. Anosov Pdf

This volume is devoted to the "hyperbolic theory" of dynamical systems (DS), that is, the theory of smooth DS's with hyperbolic behaviour of the tra jectories (generally speaking, not the individual trajectories, but trajectories filling out more or less "significant" subsets in the phase space. Hyperbolicity the property that under a small displacement of any of a trajectory consists in point of it to one side of the trajectory, the change with time of the relative positions of the original and displaced points resulting from the action of the DS is reminiscent of the mot ion next to a saddle. If there are "sufficiently many" such trajectories and the phase space is compact, then although they "tend to diverge from one another" as it were, they "have nowhere to go" and their behaviour acquires a complicated intricate character. (In the physical literature one often talks about "chaos" in such situations. ) This type of be haviour would appear to be the opposite of the more customary and simple type of behaviour characterized by its own kind of stability and regularity of the motions (these words are for the moment not being used as a strict ter 1 minology but rather as descriptive informal terms). The ergodic properties of DS's with hyperbolic behaviour of trajectories (Bunimovich et al. 1985) have already been considered in Volume 2 of this series. In this volume we therefore consider mainly the properties of a topological character (see below 2 for further details).

Author : Michael Atiyah,Daniel Iagolnitzer
Publisher : World Scientific
Page : 644 pages
File Size : 48,7 Mb
Release : 1997-10-13
Category : Mathematics
ISBN : 9789814497510

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Fields Medallists' Lectures by Michael Atiyah,Daniel Iagolnitzer Pdf

Although the Fields Medal does not have the same public recognition as the Nobel Prizes, they share a similar intellectual standing. It is restricted to one field - that of mathematics - and an age limit of 40 has become an accepted tradition. Mathematics has in the main been interpreted as pure mathematics, and this is not so unreasonable since major contributions in some applied areas can be (and have been) recognized with Nobel Prizes. The restriction to 40 years is of marginal significance, since most mathematicians have made their mark long before this age.A list of Fields Medallists and their contributions provides a bird's eye view of mathematics over the past 60 years. It highlights the areas in which, at various times, greatest progress has been made. This volume does not pretend to be comprehensive, nor is it a historical document. On the other hand, it presents contributions from 22 Fields Medallists and so provides a highly interesting and varied picture.The contributions themselves represent the choice of the individual Medallists. In some cases the articles relate directly to the work for which the Fields Medals were awarded. In other cases new articles have been produced which relate to more current interests of the Medallists. This indicates that while Fields Medallists must be under 40 at the time of the award, their mathematical development goes well past this age. In fact the age limit of 40 was chosen so that young mathematicians would be encouraged in their future work.The Fields Medallists' Lectures is now available on CD-ROM. Sections can be accessed at the touch of a button, and similar topics grouped together using advanced keyword searches.

Author : Michael Atiyah,Daniel Iagolnitzer
Publisher : World Scientific
Page : 824 pages
File Size : 51,5 Mb
Release : 2003-11-03
Category : Mathematics
ISBN : 9789814486804

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Fields Medallists' Lectures, 2nd Edition by Michael Atiyah,Daniel Iagolnitzer Pdf

Although the Fields Medal does not have the same public recognition as the Nobel Prizes, they share a similar intellectual standing. It is restricted to one field — that of mathematics — and an age limit of 40 has become an accepted tradition. Mathematics has in the main been interpreted as pure mathematics, and this is not so unreasonable since major contributions in some applied areas can be (and have been) recognized with Nobel Prizes.A list of Fields Medallists and their contributions provides a bird's-eye view of mathematics over the past 60 years. It highlights the areas in which, at various times, greatest progress has been made. This volume does not pretend to be comprehensive, nor is it a historical document. On the other hand, it presents contributions from Fields Medallists and so provides a highly interesting and varied picture.The second edition of Fields Medallists' Lectures features additional contributions from the following Medallists: Kunihiko Kodaira (1954), Richard E Borcherds (1998), William T Gowers (1998), Maxim Kontsevich (1998), Curtis T McMullen (1998) and Vladimir Voevodsky (2002).

Author : Daniel Iagolnitzer
Publisher : World Scientific
Page : 824 pages
File Size : 51,8 Mb
Release : 2003
Category : Mathematics
ISBN : 9789812382597

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Fields Medallists' Lectures by Daniel Iagolnitzer Pdf

Although the Fields Medal does not have the same public recognition as the Nobel Prizes, they share a similar intellectual standing. It is restricted to the field of mathematics and an age limit of 40 has become an accepted tradition. This volume presents contributions from Fields Medallists.

Author : Anonim
Publisher : Springer Nature
Page : 876 pages
File Size : 44,5 Mb
Release : 2024-05-06
Category : Electronic
ISBN : 9783031339738

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by Anonim Pdf