Geodesic Flows
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Geodesic Flows
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Author : Gabriel P. Paternain
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Geodesic Flows written by Gabriel P. Paternain 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 2012-12-06 with Mathematics categories.
The aim of this book is to present the fundamental concepts and properties of the geodesic flow of a closed Riemannian manifold. The topics covered are close to my research interests. An important goal here is to describe properties of the geodesic flow which do not require curvature assumptions. A typical example of such a property and a central result in this work is Mane's formula that relates the topological entropy of the geodesic flow with the exponential growth rate of the average numbers of geodesic arcs between two points in the manifold. The material here can be reasonably covered in a one-semester course. I have in mind an audience with prior exposure to the fundamentals of Riemannian geometry and dynamical systems. I am very grateful for the assistance and criticism of several people in preparing the text. In particular, I wish to thank Leonardo Macarini and Nelson Moller who helped me with the writing of the first two chapters and the figures. Gonzalo Tomaria caught several errors and contributed with helpful suggestions. Pablo Spallanzani wrote solutions to several of the exercises. I have used his solutions to write many of the hints and answers. I also wish to thank the referee for a very careful reading of the manuscript and for a large number of comments with corrections and suggestions for improvement.
Flows On 2 Dimensional Manifolds
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Author : Igor Nikolaev
language : en
Publisher: Springer Science & Business Media
Release Date : 1999-07-15
Flows On 2 Dimensional Manifolds written by Igor Nikolaev 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 1999-07-15 with Language Arts & Disciplines categories.
Time-evolution in low-dimensional topological spaces is a subject of puzzling vitality. This book is a state-of-the-art account, covering classical and new results. The volume comprises Poincaré-Bendixson, local and Morse-Smale theories, as well as a carefully written chapter on the invariants of surface flows. Of particular interest are chapters on the Anosov-Weil problem, C*-algebras and non-compact surfaces. The book invites graduate students and non-specialists to a fascinating realm of research. It is a valuable source of reference to the specialists.
Geometry Of The Generalized Geodesic Flow And Inverse Spectral Problems
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Author : Vesselin M. Petkov
language : en
Publisher: John Wiley & Sons
Release Date : 2017-01-30
Geometry Of The Generalized Geodesic Flow And Inverse Spectral Problems written by Vesselin M. Petkov and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-30 with Mathematics categories.
This book is a new edition of a title originally published in1992. No other book has been published that treats inverse spectral and inverse scattering results by using the so called Poisson summation formula and the related study of singularities. This book presents these in a closed and comprehensive form, and the exposition is based on a combination of different tools and results from dynamical systems, microlocal analysis, spectral and scattering theory. The content of the first edition is still relevant, however the new edition will include several new results established after 1992; new text will comprise about a third of the content of the new edition. The main chapters in the first edition in combination with the new chapters will provide a better and more comprehensive presentation of importance for the applications inverse results. These results are obtained by modern mathematical techniques which will be presented together in order to give the readers the opportunity to completely understand them. Moreover, some basic generic properties established by the authors after the publication of the first edition establishing the wide range of applicability of the Poison relation will be presented for first time in the new edition of the book.
Partially Hyperbolic Dynamics Laminations And Teichmuller Flow
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Author : Giovanni Forni
language : en
Publisher: American Mathematical Soc.
Release Date :
Partially Hyperbolic Dynamics Laminations And Teichmuller Flow written by Giovanni Forni 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.
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.
Integrable Geodesic Flows On Two Dimensional Surfaces
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Author : A.V. Bolsinov
language : en
Publisher: Springer
Release Date : 2000
Integrable Geodesic Flows On Two Dimensional Surfaces written by A.V. Bolsinov and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
From Moscow State University, Bolsinov (computer methods) and Fomenko (differential geometry) present a new approach to the qualitative analysis of the particular type of geodesic flow of Riemannian metrics on manifolds based on the theory of topological classification of integrable Hamiltonian systems. They begin by introducing the qualitative theory of integrable Hamiltonian systems, then discuss the class of integrable geodesic flows on two-dimensional surfaces from both the classical and contemporary perspectives. They classify the flows according to equivalence relations, such as isometry, the Liouville equivalence, the smooth and continuous trajectory equivalence, and the geodesic equivalence. They also explain the new technique that makes such classification possible. Many of their results have not been published before. The Russian original is Geometriia i topologiia integriruemykh geodezicheskikh potokov na poverkhnostiakhAnnotation copyrighted by Book News, Inc., Portland, OR
Geodesic Flows On Closed Riemann Manifolds With Negative Curvature
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Author : D. V. Anosov
language : en
Publisher:
Release Date : 1969
Geodesic Flows On Closed Riemann Manifolds With Negative Curvature written by D. V. Anosov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Mathematics categories.
An Introduction To Symbolic Dynamics And Coding
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Author : Douglas A. Lind
language : en
Publisher: Cambridge University Press
Release Date : 2021-01-21
An Introduction To Symbolic Dynamics And Coding written by Douglas A. Lind 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 2021-01-21 with Language Arts & Disciplines categories.
Elementary introduction to symbolic dynamics, updated to describe the main advances in the subject since the original publication in 1995.
Integrable Hamiltonian Systems
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Author : A.V. Bolsinov
language : en
Publisher: CRC Press
Release Date : 2004-02-25
Integrable Hamiltonian Systems written by A.V. Bolsinov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-25 with Mathematics categories.
Integrable Hamiltonian systems have been of growing interest over the past 30 years and represent one of the most intriguing and mysterious classes of dynamical systems. This book explores the topology of integrable systems and the general theory underlying their qualitative properties, singularites, and topological invariants. The authors,
Encyclopedic Dictionary Of Mathematics
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Author : Nihon Sūgakkai
language : en
Publisher: MIT Press
Release Date : 1993
Encyclopedic Dictionary Of Mathematics written by Nihon Sūgakkai and has been published by MIT Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with Mathematics categories.
V.1. A.N. v.2. O.Z. Apendices and indexes.
Introduction To The Modern Theory Of Dynamical Systems
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Author : Anatole Katok
language : en
Publisher: Cambridge University Press
Release Date : 1995
Introduction To The Modern Theory Of Dynamical Systems 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 1995 with Mathematics categories.
This book provided the first self-contained comprehensive exposition of the theory of dynamical systems as a core mathematical discipline closely intertwined with most of the main areas of mathematics. The authors introduce and rigorously develop the theory while providing researchers interested in applications with fundamental tools and paradigms. The book begins with a discussion of several elementary but fundamental examples. These are used to formulate a program for the general study of asymptotic properties and to introduce the principal theoretical concepts and methods. The main theme of the second part of the book is the interplay between local analysis near individual orbits and the global complexity of the orbit structure. The third and fourth parts develop the theories of low-dimensional dynamical systems and hyperbolic dynamical systems in depth. Over 400 systematic exercises are included in the text. The book is aimed at students and researchers in mathematics at all levels from advanced undergraduate up.