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Geodesic Flows
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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.
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.
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.
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 442 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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
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
Book Synopsis Geometrical Theory Of Dynamical Systems And Fluid Flows (Revised Edition) by : Tsutomu (Jixin) Kambe
Download or read book Geometrical Theory Of Dynamical Systems And Fluid Flows (Revised Edition) written by Tsutomu (Jixin) Kambe and published by World Scientific Publishing Company. This book was released on 2009-12-28 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory textbook on the geometrical theory of dynamical systems, fluid flows and certain integrable systems. The topics are interdisciplinary and extend from mathematics, mechanics and physics to mechanical engineering, and the approach is very fundamental. The main theme of this book is a unified formulation to understand dynamical evolutions of physical systems within mathematical ideas of Riemannian geometry and Lie groups by using well-known examples. Underlying mathematical concepts include transformation invariance, covariant derivative, geodesic equation and curvature tensors on the basis of differential geometry, theory of Lie groups and integrability. These mathematical theories are applied to physical systems such as free rotation of a top, surface wave of shallow water, action principle in mechanics, diffeomorphic flow of fluids, vortex motions and some integrable systems.In the latest edition, a new formulation of fluid flows is also presented in a unified fashion on the basis of the gauge principle of theoretical physics and principle of least action along with new type of Lagrangians. A great deal of effort has been directed toward making the description elementary, clear and concise, to provide beginners easy access to the topics.
Book Synopsis Group Representations, Ergodic Theory, Operator Algebras, and Mathematical Physics by : Calvin C. Moore
Download or read book Group Representations, Ergodic Theory, Operator Algebras, and Mathematical Physics written by Calvin C. Moore and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Mathematical Sciences Research Institute sponsored a three day conference, May 21-23, 1984 to honor Professor George W. Mackey. The title of the conference, Group Representations, Ergodic Theory, Operator Algebras, and Mathematical Physics, reflects the interests in science that have characterized Professor wide ranging Mackey's work. The conference provided an opportunity for his students, friends and colleagues to honor him and his contributions. The conference was attended by over one hundred people and the participants included five mathematical generations Professor Mackey's mathematical father, Marshall Stone, many mathematical children, grandchildren, and at least one mathematical great-grandchild. This volume is a compendium of the scientific papers presented at the conference plus some additional papers contributed after the conference. The far ranging scope of the various articles is a further indication of the large number of fields that have been affected by Professor Mackey's work. Calvin C. Moore Berkeley, CA Feb, 1986 Table of Contents Preface vi i Ambiguity Functions and Group L. Auslander and Representations R. Tolimieri Kirillov Orbits and Direct Integral Lawrence Corwin 11 Decompositions on Certain Quotient Spaces Some Homotopy and Shape Calculations Edward G. Effors and 69 for C*-Algebras Jerome Kaminker 121 Small Unitary Representations of Roger Howe Classical Groups Dual Vector Spaces Irving Kaplansky 151 Exponential Decay of Correlation Calvin C. Moore 163 Coefficients for Geodesic Flows Lattices in U(n. I) G. D. Mostow Induced Bundles and Nonlinear Irving E. Segal 199 Wave equations Compact Ahelian Aut.
Book Synopsis Manifolds all of whose Geodesics are Closed by : A. L. Besse
Download or read book Manifolds all of whose Geodesics are Closed written by A. L. Besse and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 271 pages. Available in PDF, EPUB and Kindle. Book excerpt: X 1 O S R Cher lecteur, J'entre bien tard dans la sphere etroite des ecrivains au double alphabet, moi qui, il y a plus de quarante ans deja, avais accueilli sur mes terres un general epris de mathematiques. JI m'avait parle de ses projets grandioses en promettant d'ailleurs de m'envoyer ses ouvrages de geometrie. Je suis entiche de geometrie et c'est d'elle dontje voudrais vous parler, oh! certes pas de toute la geometrie, mais de celle que fait l'artisan qui taille, burine, amene, gauchit, peaufine les formes. Mon interet pour le probleme dont je veux vous entretenir ici, je le dois a un ami ebeniste. En effet comme je rendais un jour visite il cet ami, je le trouvai dans son atelier affaire a un tour. Il se retourna bientot, puis, rayonnant, me tendit une sorte de toupie et me dit: {laquo}Monsieur Besse, vous qui calculez les formes avec vos grimoires, que pensez-vous de ceci?)) Je le regardai interloque. Il poursuivit: {laquo}Regardez! Si vous prenez ce collier de laine et si vous le maintenez fermement avec un doigt place n'importe ou sur la toupie, eh bien! la toupie passera toujours juste en son interieur, sans laisser le moindre espace.)) Je rentrai chez moi, fort etonne, car sa toupie etait loin d'etre une boule. Je me mis alors au travail ...
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.
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.
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.
Book Synopsis Contemporary Geometry And Related Topics, Proceedings Of The Workshop by : Neda Bokan
Download or read book Contemporary Geometry And Related Topics, Proceedings Of The Workshop written by Neda Bokan and published by World Scientific. This book was released on 2004-03-15 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume covers a broad range of subjects in modern geometry and related branches of mathematics, physics and computer science. Most of the papers show new, interesting results in Riemannian geometry, homotopy theory, theory of Lie groups and Lie algebras, topological analysis, integrable systems, quantum groups, and noncommutative geometry. There are also papers giving overviews of the recent achievements in some special topics, such as the Willmore conjecture, geodesic mappings, Weyl's tube formula, and integrable geodesic flows. This book provides a great chance for interchanging new results and ideas in multidisciplinary studies.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences
Book Synopsis Robust Chaos And Its Applications by : Zeraoulia Elhadj
Download or read book Robust Chaos And Its Applications written by Zeraoulia Elhadj and published by World Scientific. This book was released on 2011-10-17 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: Robust chaos is defined by the absence of periodic windows and coexisting attractors in some neighborhoods in the parameter space of a dynamical system. This unique book explores the definition, sources, and roles of robust chaos. The book is written in a reasonably self-contained manner and aims to provide students and researchers with the necessary understanding of the subject. Most of the known results, experiments, and conjectures about chaos in general and about robust chaos in particular are collected here in a pedagogical form. Many examples of dynamical systems, ranging from purely mathematical to natural and social processes displaying robust chaos, are discussed in detail. At the end of each chapter is a set of exercises and open problems (more than 260 in the whole book) intended to reinforce the ideas and provide additional experiences for both readers and researchers in nonlinear science in general, and chaos theory in particular./a
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.
Book Synopsis Geometry and Nature by : William Kingdon Clifford
Download or read book Geometry and Nature written by William Kingdon Clifford and published by American Mathematical Soc.. This book was released on 1997 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the outgrowth of a conference devoted to William K. Clifford entitled, "New Trends in Geometrical and Topological Methods", which was held at the University of Madeira in July and August 1995. The aim of the conference was to bring together active workers in fields linked to Clifford's work and to foster the exchange of ideas between mathematicians and theoretical physicists. Divided into 6 one-day sessions, each session was devoted to a specific aspect of Clifford's work. This volume is an attempt to bring the Clifford legacy in a new perspective to a larger community of mathematicians and physicists. New concepts, ideas, and results stemming from Clifford's work are discussed. Containing papers presented or submitted to the conference, each article is self-contained.
Book Synopsis An Introduction to Contact Topology by : Hansjörg Geiges
Download or read book An Introduction to Contact Topology written by Hansjörg Geiges and published by Cambridge University Press. This book was released on 2008-03-13 with total page 8 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text on contact topology is a comprehensive introduction to the subject, including recent striking applications in geometric and differential topology: Eliashberg's proof of Cerf's theorem via the classification of tight contact structures on the 3-sphere, and the Kronheimer-Mrowka proof of property P for knots via symplectic fillings of contact 3-manifolds. Starting with the basic differential topology of contact manifolds, all aspects of 3-dimensional contact manifolds are treated in this book. One notable feature is a detailed exposition of Eliashberg's classification of overtwisted contact structures. Later chapters also deal with higher-dimensional contact topology. Here the focus is on contact surgery, but other constructions of contact manifolds are described, such as open books or fibre connected sums. This book serves both as a self-contained introduction to the subject for advanced graduate students and as a reference for researchers.
