Geodesic Flows

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Geodesic Flows

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Author : Gabriel P. Paternain
Publisher : Springer Science & Business Media
ISBN 13 : 1461216001
Total Pages : 160 pages
Book Rating : 4.4/5 (612 download)

Book Synopsis Geodesic Flows by : Gabriel P. Paternain

Download or read book Geodesic Flows written by Gabriel P. Paternain and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Two Classes of Riemannian Manifolds Whose Geodesic Flows Are Integrable

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Author : Kazuyoshi Kiyohara
Publisher : American Mathematical Soc.
ISBN 13 : 0821806408
Total Pages : 159 pages
Book Rating : 4.8/5 (218 download)

Book Synopsis Two Classes of Riemannian Manifolds Whose Geodesic Flows Are Integrable by : Kazuyoshi Kiyohara

Download or read book Two Classes of Riemannian Manifolds Whose Geodesic Flows Are Integrable written by Kazuyoshi Kiyohara and published by American Mathematical Soc.. This book was released on 1997 with total page 159 pages. Available in PDF, EPUB and Kindle. Book excerpt: Two classes of manifolds whose geodesic flows are integrable are defined, and their global structures are investigated. They are called Liouville manifolds and Kahler-Liouville manifolds respectively. In each case, the author finds several invariants with which they are partly classified. The classification indicates, in particular, that these classes contain many new examples of manifolds with integrable geodesic flow.

Elements of Topological Dynamics

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Author : J. de Vries
Publisher : Springer Science & Business Media
ISBN 13 : 9780792322870
Total Pages : 772 pages
Book Rating : 4.3/5 (228 download)

Book Synopsis Elements of Topological Dynamics by : J. de Vries

Download or read book Elements of Topological Dynamics written by J. de Vries and published by Springer Science & Business Media. This book was released on 1993-06-30 with total page 772 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed as an introduction into what I call 'abstract' Topological Dynamics (TO): the study of topological transformation groups with respect to problems that can be traced back to the qualitative theory of differential equa is in the tradition of the books [GH] and [EW. The title tions. So this book (,Elements . . . ' rather than 'Introduction . . . ') does not mean that this book should be compared, either in scope or in (intended) impact, with the 'Ele ments' of Euclid or Bourbaki. Instead, it reflects the choice and organisation of the material in this book: elementary and basic (but sufficient to understand recent research papers in this field). There are still many challenging prob lems waiting for a solution, and especially among general topologists there is a growing interest in this direction. However, the technical inaccessability of many research papers makes it almost impossible for an outsider to under stand what is going on. To a large extent, this inaccessability is caused by the lack of a good and systematic exposition of the fundamental methods and techniques of abstract TO. This book is an attempt to fill this gap. The guiding principle for the organization of the material in this book has been the exposition of methods and techniques rather than a discussion of the leading problems and their solutions. though the latter are certainly not neglected: they are used as a motivation wherever possible.

Geometry of the Generalized Geodesic Flow and Inverse Spectral Problems

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Author : Vesselin M. Petkov
Publisher : John Wiley & Sons
ISBN 13 : 1119107660
Total Pages : 428 pages
Book Rating : 4.1/5 (191 download)

Book Synopsis Geometry of the Generalized Geodesic Flow and Inverse Spectral Problems by : Vesselin M. Petkov

Download or read book Geometry of the Generalized Geodesic Flow and Inverse Spectral Problems written by Vesselin M. Petkov and published by John Wiley & Sons. This book was released on 2017-01-30 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Integrable Geodesic Flows on Two-Dimensional Surfaces

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Author : A.V. Bolsinov
Publisher : Springer
ISBN 13 :
Total Pages : 344 pages
Book Rating : 4.3/5 (91 download)

Book Synopsis Integrable Geodesic Flows on Two-Dimensional Surfaces by : A.V. Bolsinov

Download or read book Integrable Geodesic Flows on Two-Dimensional Surfaces written by A.V. Bolsinov and published by Springer. This book was released on 2000 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Integrable Hamiltonian Systems

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Author : A.V. Bolsinov
Publisher : CRC Press
ISBN 13 : 0203643429
Total Pages : 752 pages
Book Rating : 4.2/5 (36 download)

Book Synopsis Integrable Hamiltonian Systems by : A.V. Bolsinov

Download or read book Integrable Hamiltonian Systems written by A.V. Bolsinov and published by CRC Press. This book was released on 2004-02-25 with total page 752 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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,

Geodesy - the Challenge of the 3rd Millennium

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Author : Erik Grafarend
Publisher : Springer Science & Business Media
ISBN 13 : 3662052962
Total Pages : 460 pages
Book Rating : 4.6/5 (62 download)

Book Synopsis Geodesy - the Challenge of the 3rd Millennium by : Erik Grafarend

Download or read book Geodesy - the Challenge of the 3rd Millennium written by Erik Grafarend and published by Springer Science & Business Media. This book was released on 2013-12-11 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geodesy as the science which determines the figure of the earth, its orientation in space and its gravity field as well as its temporal changes, produces key elements in describing the kinematics and the dynamics of the deformable body "earth". It contributes in particular to geodynamics and opens the door to decode the complex interactions between components of "the system earth". In the breathtaking development recently a whole arsenal of new terrestrial, airborne as well as satelliteborne measurement techniques for earth sciences have been made available and have broadened the spectrum of measurable earth parameters with an unforeseen accuracy and precision, in particular to resolve the factor time. The book focusses on these topics and gives a state of the art of modern geodesy.

Introduction to the Modern Theory of Dynamical Systems

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Author : Anatole Katok
Publisher : Cambridge University Press
ISBN 13 : 9780521575577
Total Pages : 828 pages
Book Rating : 4.5/5 (755 download)

Book Synopsis Introduction to the Modern Theory of Dynamical Systems by : Anatole Katok

Download or read book Introduction to the Modern Theory of Dynamical Systems written by Anatole Katok and published by Cambridge University Press. This book was released on 1995 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Geodesic and Horocyclic Trajectories

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Author : Françoise Dal’Bo
Publisher : Springer Science & Business Media
ISBN 13 : 0857290738
Total Pages : 181 pages
Book Rating : 4.8/5 (572 download)

Book Synopsis Geodesic and Horocyclic Trajectories by : Françoise Dal’Bo

Download or read book Geodesic and Horocyclic Trajectories written by Françoise Dal’Bo and published by Springer Science & Business Media. This book was released on 2010-11-12 with total page 181 pages. Available in PDF, EPUB and Kindle. Book excerpt: Geodesic and Horocyclic Trajectories presents an introduction to the topological dynamics of two classical flows associated with surfaces of curvature −1, namely the geodesic and horocycle flows. Written primarily with the idea of highlighting, in a relatively elementary framework, the existence of gateways between some mathematical fields, and the advantages of using them, historical aspects of this field are not addressed and most of the references are reserved until the end of each chapter in the Comments section. Topics within the text cover geometry, and examples, of Fuchsian groups; topological dynamics of the geodesic flow; Schottky groups; the Lorentzian point of view and Trajectories and Diophantine approximations.

Geodesic Flows on Closed Riemann Manifolds with Negative Curvature

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Author : D. V. Anosov
Publisher :
ISBN 13 :
Total Pages : 444 pages
Book Rating : 4.:/5 (321 download)

Book Synopsis Geodesic Flows on Closed Riemann Manifolds with Negative Curvature by : D. V. Anosov

Download or read book Geodesic Flows on Closed Riemann Manifolds with Negative Curvature written by D. V. Anosov and published by . This book was released on 1969 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Hamiltonian Dynamical Systems

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Author : H.S. Dumas
Publisher : Springer Science & Business Media
ISBN 13 : 9780387944371
Total Pages : 418 pages
Book Rating : 4.9/5 (443 download)

Book Synopsis Hamiltonian Dynamical Systems by : H.S. Dumas

Download or read book Hamiltonian Dynamical Systems written by H.S. Dumas and published by Springer Science & Business Media. This book was released on 1995-03-10 with total page 418 pages. Available in PDF, EPUB and Kindle. Book excerpt: From its origins nearly two centuries ago, Hamiltonian dynamics has grown to embrace the physics of nearly all systems that evolve without dissipation, as well as a number of branches of mathematics, some of which were literally created along the way. This volume contains the proceedings of the International Conference on Hamiltonian Dynamical Systems; its contents reflect the wide scope and increasing influence of Hamiltonian methods, with contributions from a whole spectrum of researchers in mathematics and physics from more than half a dozen countries, as well as several researchers in the history of science. With the inclusion of several historical articles, this volume is not only a slice of state-of-the-art methodology in Hamiltonian dynamics, but also a slice of the bigger picture in which that methodology is imbedded.

Dynamical Systems

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Author : Albert Fathi
Publisher : Cambridge University Press
ISBN 13 : 0521860687
Total Pages : 597 pages
Book Rating : 4.5/5 (218 download)

Book Synopsis Dynamical Systems by : Albert Fathi

Download or read book Dynamical Systems written by Albert Fathi and published by Cambridge University Press. This book was released on 2006-02-02 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of up-to-date research and classic papers reflecting the work of Michael Herman.

Geometric Methods in Physics XXXV

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Author : Piotr Kielanowski
Publisher : Birkhäuser
ISBN 13 : 3319635948
Total Pages : 282 pages
Book Rating : 4.3/5 (196 download)

Book Synopsis Geometric Methods in Physics XXXV by : Piotr Kielanowski

Download or read book Geometric Methods in Physics XXXV written by Piotr Kielanowski and published by Birkhäuser. This book was released on 2018-02-10 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book features a selection of articles based on the XXXV Białowieża Workshop on Geometric Methods in Physics, 2016. The series of Białowieża workshops, attended by a community of experts at the crossroads of mathematics and physics, is a major annual event in the field. The works in this book, based on presentations given at the workshop, are previously unpublished, at the cutting edge of current research, typically grounded in geometry and analysis, and with applications to classical and quantum physics. In 2016 the special session "Integrability and Geometry" in particular attracted pioneers and leading specialists in the field. Traditionally, the Białowieża Workshop is followed by a School on Geometry and Physics, for advanced graduate students and early-career researchers, and the book also includes extended abstracts of the lecture series.

Progress in Inverse Spectral Geometry

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Author : Stig I. Andersson
Publisher : Birkhäuser
ISBN 13 : 3034889380
Total Pages : 202 pages
Book Rating : 4.0/5 (348 download)

Book Synopsis Progress in Inverse Spectral Geometry by : Stig I. Andersson

Download or read book Progress in Inverse Spectral Geometry written by Stig I. Andersson and published by Birkhäuser. This book was released on 2012-12-06 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most polynomial growth on every half-space Re (z) ::::: c. Moreover, Op(t) depends holomorphically on t for Re t> O. General references for much of the material on the derivation of spectral functions, asymptotic expansions and analytic properties of spectral functions are [A-P-S] and [Sh], especially Chapter 2. To study the spectral functions and their relation to the geometry and topology of X, one could, for example, take the natural associated parabolic problem as a starting point. That is, consider the 'heat equation': (%t + p) u(x, t) = 0 { u(x, O) = Uo(x), tP which is solved by means of the (heat) semi group V(t) = e- ; namely, u(·, t) = V(t)uoU· Assuming that V(t) is of trace class (which is guaranteed, for instance, if P has a positive principal symbol), it has a Schwartz kernel K E COO(X x X x Rt, E* ®E), locally given by 00 K(x, y; t) = L>-IAk(~k ® 'Pk)(X, y), k=O for a complete set of orthonormal eigensections 'Pk E COO(E). Taking the trace, we then obtain: 00 tA Op(t) = trace(V(t)) = 2::>- k. k=O Now, using, e. g., the Dunford calculus formula (where C is a suitable curve around a(P)) as a starting point and the standard for malism of pseudodifferential operators, one easily derives asymptotic expansions for the spectral functions, in this case for Op.

Geodesic Flows

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Author : Gabriel Pedro Paternain
Publisher : Birkhauser
ISBN 13 : 9783764341442
Total Pages : 149 pages
Book Rating : 4.3/5 (414 download)

Book Synopsis Geodesic Flows by : Gabriel Pedro Paternain

Download or read book Geodesic Flows written by Gabriel Pedro Paternain and published by Birkhauser. This book was released on 1999-01-01 with total page 149 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This self-contained monograph will be of interest to graduate students and researchers of dynamical systems and differential geometry. Numerous exercises and examples as well as a comprehensive index and bibliography make this work an excellent self-study resource or text for a one-semester course or seminar."--BOOK JACKET

In the Tradition of Thurston

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Author : Ken’ichi Ohshika
Publisher : Springer Nature
ISBN 13 : 3030559289
Total Pages : 724 pages
Book Rating : 4.0/5 (35 download)

Book Synopsis In the Tradition of Thurston by : Ken’ichi Ohshika

Download or read book In the Tradition of Thurston written by Ken’ichi Ohshika and published by Springer Nature. This book was released on 2020-12-07 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of 16 surveys on Thurston's work and its later development. The authors are mathematicians who were strongly influenced by Thurston's publications and ideas. The subjects discussed include, among others, knot theory, the topology of 3-manifolds, circle packings, complex projective structures, hyperbolic geometry, Kleinian groups, foliations, mapping class groups, Teichmüller theory, anti-de Sitter geometry, and co-Minkowski geometry. The book is addressed to researchers and students who want to learn about Thurston’s wide-ranging mathematical ideas and their impact. At the same time, it is a tribute to Thurston, one of the greatest geometers of all time, whose work extended over many fields in mathematics and who had a unique way of perceiving forms and patterns, and of communicating and writing mathematics.

Classical Mechanics and Dynamical Systems

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Author : Conference Board of the Mathematical Sciences
Publisher : CRC Press
ISBN 13 : 9780824715298
Total Pages : 260 pages
Book Rating : 4.7/5 (152 download)

Book Synopsis Classical Mechanics and Dynamical Systems by : Conference Board of the Mathematical Sciences

Download or read book Classical Mechanics and Dynamical Systems written by Conference Board of the Mathematical Sciences and published by CRC Press. This book was released on 1981-09-01 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: