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Dynamics Beyond Uniform Hyperbolicity

Author: Christian Bonatti

Publisher: Springer Science & Business Media

Published: 2006-03-30

Total Pages: 390

ISBN-13: 3540268448

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What is Dynamics about? In broad terms, the goal of Dynamics is to describe the long term evolution of systems for which an "infinitesimal" evolution rule is known. Examples and applications arise from all branches of science and technology, like physics, chemistry, economics, ecology, communications, biology, computer science, or meteorology, to mention just a few. These systems have in common the fact that each possible state may be described by a finite (or infinite) number of observable quantities, like position, velocity, temperature, concentration, population density, and the like. Thus, m the space of states (phase space) is a subset M of an Euclidean space M . Usually, there are some constraints between these quantities: for instance, for ideal gases pressure times volume must be proportional to temperature. Then the space M is often a manifold, an n-dimensional surface for some n

Book Synopsis Dynamics Beyond Uniform Hyperbolicity by : Christian Bonatti

Download or read book Dynamics Beyond Uniform Hyperbolicity written by Christian Bonatti and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 390 pages. Available in PDF, EPUB and Kindle. Book excerpt: What is Dynamics about? In broad terms, the goal of Dynamics is to describe the long term evolution of systems for which an "infinitesimal" evolution rule is known. Examples and applications arise from all branches of science and technology, like physics, chemistry, economics, ecology, communications, biology, computer science, or meteorology, to mention just a few. These systems have in common the fact that each possible state may be described by a finite (or infinite) number of observable quantities, like position, velocity, temperature, concentration, population density, and the like. Thus, m the space of states (phase space) is a subset M of an Euclidean space M . Usually, there are some constraints between these quantities: for instance, for ideal gases pressure times volume must be proportional to temperature. Then the space M is often a manifold, an n-dimensional surface for some n

Dynamics Beyond Uniform Hyperbolicity

Author: Christian Bonatti

Publisher:

Published: 2003

Total Pages: 205

ISBN-13:

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Book Synopsis Dynamics Beyond Uniform Hyperbolicity by : Christian Bonatti

Download or read book Dynamics Beyond Uniform Hyperbolicity written by Christian Bonatti and published by . This book was released on 2003 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Dynamics Beyond Uniform Hyperbolicity

Author: Christian Bonatti

Publisher:

Published: 2005

Total Pages: 384

ISBN-13:

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Book Synopsis Dynamics Beyond Uniform Hyperbolicity by : Christian Bonatti

Download or read book Dynamics Beyond Uniform Hyperbolicity written by Christian Bonatti and published by . This book was released on 2005 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Dynamical Systems, Ergodic Theory and Applications

Author: L.A. Bunimovich

Publisher: Springer

Published: 2000-04-05

Total Pages: 460

ISBN-13: 9783540663164

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This EMS volume, the first edition of which was published as Dynamical Systems II, EMS 2, familiarizes the reader with the fundamental ideas and results of modern ergodic theory and its applications to dynamical systems and statistical mechanics. The enlarged and revised second edition adds two new contributions on ergodic theory of flows on homogeneous manifolds and on methods of algebraic geometry in the theory of interval exchange transformations.

Book Synopsis Dynamical Systems, Ergodic Theory and Applications by : L.A. Bunimovich

Download or read book Dynamical Systems, Ergodic Theory and Applications written by L.A. Bunimovich and published by Springer. This book was released on 2000-04-05 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This EMS volume, the first edition of which was published as Dynamical Systems II, EMS 2, familiarizes the reader with the fundamental ideas and results of modern ergodic theory and its applications to dynamical systems and statistical mechanics. The enlarged and revised second edition adds two new contributions on ergodic theory of flows on homogeneous manifolds and on methods of algebraic geometry in the theory of interval exchange transformations.

Partially Hyperbolic Dynamics, Laminations, and Teichmuller Flow

Author: Giovanni Forni

Publisher: American Mathematical Soc.

Published: 2007

Total Pages: 354

ISBN-13: 0821842749

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This volume collects a set of contributions by participants of the Workshop Partially hyperbolic dynamics, laminations, and Teichmuller flow held at the Fields Institute in Toronto in January 2006. The Workshop brought together several leading experts in two very active fields of contemporary dynamical systems theory: partially hyperbolic dynamics and Teichmuller dynamics. They are unified by ideas coming from the theory of laminations and foliations, dynamical hyperbolicity, and ergodic theory. These are the main themes of the current volume. The volume contains both surveys and research papers on non-uniform and partial hyperbolicity, on dominated splitting and beyond (in Part I), Teichmuller dynamics with applications to interval exchange transformations and on the topology of moduli spaces of quadratic differentials (in Part II), foliations and laminations and other miscellaneous papers (in Part III). Taken together these papers provide a snapshot of the state of the art in some of the most active topics at the crossroads between dynamical systems, smooth ergodic theory, geometry and topology, suitable for advanced graduate students and researchers.Non-specialists will find the extensive, in-depth surveys especially useful.

Book Synopsis Partially Hyperbolic Dynamics, Laminations, and Teichmuller Flow by : Giovanni Forni

Download or read book Partially Hyperbolic Dynamics, Laminations, and Teichmuller Flow written by Giovanni Forni and published by American Mathematical Soc.. This book was released on 2007 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume collects a set of contributions by participants of the Workshop Partially hyperbolic dynamics, laminations, and Teichmuller flow held at the Fields Institute in Toronto in January 2006. The Workshop brought together several leading experts in two very active fields of contemporary dynamical systems theory: partially hyperbolic dynamics and Teichmuller dynamics. They are unified by ideas coming from the theory of laminations and foliations, dynamical hyperbolicity, and ergodic theory. These are the main themes of the current volume. The volume contains both surveys and research papers on non-uniform and partial hyperbolicity, on dominated splitting and beyond (in Part I), Teichmuller dynamics with applications to interval exchange transformations and on the topology of moduli spaces of quadratic differentials (in Part II), foliations and laminations and other miscellaneous papers (in Part III). Taken together these papers provide a snapshot of the state of the art in some of the most active topics at the crossroads between dynamical systems, smooth ergodic theory, geometry and topology, suitable for advanced graduate students and researchers.Non-specialists will find the extensive, in-depth surveys especially useful.

Non-uniform Hyperbolicity in Complex Dynamics

Author: Jacek Graczyk

Publisher:

Published: 2001

Total Pages:

ISBN-13:

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Book Synopsis Non-uniform Hyperbolicity in Complex Dynamics by : Jacek Graczyk

Download or read book Non-uniform Hyperbolicity in Complex Dynamics written by Jacek Graczyk and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Dimension and Recurrence in Hyperbolic Dynamics

Author: Luis Barreira

Publisher: Springer Science & Business Media

Published: 2008-11-05

Total Pages: 302

ISBN-13: 376438882X

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The main objective of this book is to give a broad uni?ed introduction to the study of dimension and recurrence inhyperbolic dynamics. It includes a disc- sion of the foundations, main results, and main techniques in the rich interplay of fourmain areas of research: hyperbolic dynamics, dimension theory, multifractal analysis, and quantitative recurrence. It also gives a panorama of several selected topics of current research interest. This includes topics on irregular sets, var- tional principles, applications to number theory, measures of maximal dimension, multifractal rigidity, and quantitative recurrence. The book isdirected to researchersas well as graduate students whowish to have a global view of the theory together with a working knowledgeof its main techniques. It can also be used as a basis for graduatecourses in dimension theory of dynamical systems, multifractal analysis (together with a discussion of several special topics), and pointwise dimension and recurrence in hyperbolic dynamics. I hope that the book may serve as a fast entry point to this exciting and active ?eld of research, and also that it may lead to further developments.

Book Synopsis Dimension and Recurrence in Hyperbolic Dynamics by : Luis Barreira

Download or read book Dimension and Recurrence in Hyperbolic Dynamics written by Luis Barreira and published by Springer Science & Business Media. This book was released on 2008-11-05 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main objective of this book is to give a broad uni?ed introduction to the study of dimension and recurrence inhyperbolic dynamics. It includes a disc- sion of the foundations, main results, and main techniques in the rich interplay of fourmain areas of research: hyperbolic dynamics, dimension theory, multifractal analysis, and quantitative recurrence. It also gives a panorama of several selected topics of current research interest. This includes topics on irregular sets, var- tional principles, applications to number theory, measures of maximal dimension, multifractal rigidity, and quantitative recurrence. The book isdirected to researchersas well as graduate students whowish to have a global view of the theory together with a working knowledgeof its main techniques. It can also be used as a basis for graduatecourses in dimension theory of dynamical systems, multifractal analysis (together with a discussion of several special topics), and pointwise dimension and recurrence in hyperbolic dynamics. I hope that the book may serve as a fast entry point to this exciting and active ?eld of research, and also that it may lead to further developments.

Hyperbolic Dynamics and Brownian Motion

Author: Jacques Franchi

Publisher: Oxford Mathematical Monographs

Published: 2012-08-16

Total Pages: 283

ISBN-13: 0199654107

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A simple introduction to several important fields of modern mathematics. The exposition is based on an interplay between hyperbolic geometry, stochastic calculus, special relativity and chaotic dynamics. It is suitable for anyone with some solid background in linear algebra, calculus, and probability theory.

Book Synopsis Hyperbolic Dynamics and Brownian Motion by : Jacques Franchi

Download or read book Hyperbolic Dynamics and Brownian Motion written by Jacques Franchi and published by Oxford Mathematical Monographs. This book was released on 2012-08-16 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: A simple introduction to several important fields of modern mathematics. The exposition is based on an interplay between hyperbolic geometry, stochastic calculus, special relativity and chaotic dynamics. It is suitable for anyone with some solid background in linear algebra, calculus, and probability theory.

Beyond Hyperbolicity

Author: Mark Hagen

Publisher: Cambridge University Press

Published: 2019-07-11

Total Pages: 242

ISBN-13: 1108447295

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Contains expository articles and research papers in geometric group theory focusing on generalisations of Gromov hyperbolicity.

Book Synopsis Beyond Hyperbolicity by : Mark Hagen

Download or read book Beyond Hyperbolicity written by Mark Hagen and published by Cambridge University Press. This book was released on 2019-07-11 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains expository articles and research papers in geometric group theory focusing on generalisations of Gromov hyperbolicity.

Differentiable Dynamical Systems

Author: Lan Wen

Publisher: American Mathematical Soc.

Published: 2016-07-20

Total Pages: 207

ISBN-13: 1470427990

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This is a graduate text in differentiable dynamical systems. It focuses on structural stability and hyperbolicity, a topic that is central to the field. Starting with the basic concepts of dynamical systems, analyzing the historic systems of the Smale horseshoe, Anosov toral automorphisms, and the solenoid attractor, the book develops the hyperbolic theory first for hyperbolic fixed points and then for general hyperbolic sets. The problems of stable manifolds, structural stability, and shadowing property are investigated, which lead to a highlight of the book, the Ω-stability theorem of Smale. While the content is rather standard, a key objective of the book is to present a thorough treatment for some tough material that has remained an obstacle to teaching and learning the subject matter. The treatment is straightforward and hence could be particularly suitable for self-study. Selected solutions are available electronically for instructors only. Please send email to [email protected] for more information.

Book Synopsis Differentiable Dynamical Systems by : Lan Wen

Download or read book Differentiable Dynamical Systems written by Lan Wen and published by American Mathematical Soc.. This book was released on 2016-07-20 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a graduate text in differentiable dynamical systems. It focuses on structural stability and hyperbolicity, a topic that is central to the field. Starting with the basic concepts of dynamical systems, analyzing the historic systems of the Smale horseshoe, Anosov toral automorphisms, and the solenoid attractor, the book develops the hyperbolic theory first for hyperbolic fixed points and then for general hyperbolic sets. The problems of stable manifolds, structural stability, and shadowing property are investigated, which lead to a highlight of the book, the Ω-stability theorem of Smale. While the content is rather standard, a key objective of the book is to present a thorough treatment for some tough material that has remained an obstacle to teaching and learning the subject matter. The treatment is straightforward and hence could be particularly suitable for self-study. Selected solutions are available electronically for instructors only. Please send email to [email protected] for more information.