Geodesic Flows On Closed Riemann Manifolds With Negative Curvature
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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.
Geodesic Flows On Closed Riemann Manifolda With Negative Curvature Geodezi Eskie Potoki Na Zamknutych Rimanovych Mnogoobrazijach Otricatel Noj Krivizny Engl Transl From The Russ By S Feder
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Author : Dmitrij V. Anosov
language : en
Publisher:
Release Date : 1969
Geodesic Flows On Closed Riemann Manifolda With Negative Curvature Geodezi Eskie Potoki Na Zamknutych Rimanovych Mnogoobrazijach Otricatel Noj Krivizny Engl Transl From The Russ By S Feder written by Dmitrij 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 categories.
Geometry Of Geodesics And Related Topics
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Author : Katsuhiro Shiohama
language : en
Publisher: Elsevier Science & Technology
Release Date : 1984
Geometry Of Geodesics And Related Topics written by Katsuhiro Shiohama and has been published by Elsevier Science & Technology this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Curves on surfaces categories.
This third volume in the Japanese symposia series surveys recent advances in five areas of Geometry, namely Closed geodesics, Geodesic flows, Finiteness and uniqueness theorems for compact Riemannian manifolds, Hadamard manifolds, and Topology of complete noncompact manifolds.
Geodesic Flows On Manifolds Of Negative Curvature With Smooth Horospheric Foliations
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Author : Mathematical Sciences Research Institute (Berkeley, Calif.).
language : en
Publisher:
Release Date : 1989
Geodesic Flows On Manifolds Of Negative Curvature With Smooth Horospheric Foliations written by Mathematical Sciences Research Institute (Berkeley, Calif.). and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Electronic dissertations categories.
Geodesic Flows On Manifolds Of Constant Negative Curvature
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Author : Izrailʹ Moiseevich Gelʹfand
language : en
Publisher:
Release Date : 1955
Geodesic Flows On Manifolds Of Constant Negative Curvature written by Izrailʹ Moiseevich Gelʹfand and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1955 with categories.
Ergodic Theory And Negative Curvature
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Author : Boris Hasselblatt
language : en
Publisher: Springer
Release Date : 2017-12-15
Ergodic Theory And Negative Curvature written by Boris Hasselblatt and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-12-15 with Mathematics categories.
Focussing on the mathematics related to the recent proof of ergodicity of the (Weil–Petersson) geodesic flow on a nonpositively curved space whose points are negatively curved metrics on surfaces, this book provides a broad introduction to an important current area of research. It offers original textbook-level material suitable for introductory or advanced courses as well as deep insights into the state of the art of the field, making it useful as a reference and for self-study. The first chapters introduce hyperbolic dynamics, ergodic theory and geodesic and horocycle flows, and include an English translation of Hadamard's original proof of the Stable-Manifold Theorem. An outline of the strategy, motivation and context behind the ergodicity proof is followed by a careful exposition of it (using the Hopf argument) and of the pertinent context of Teichmüller theory. Finally, some complementary lectures describe the deep connections between geodesic flows in negative curvature and Diophantine approximation.
Encyclopaedia Of Mathematics
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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-01-31
Encyclopaedia Of Mathematics written by Michiel Hazewinkel 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 1993-01-31 with Mathematics categories.
This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fme subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
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.
The Regularity Of The Linear Drift In Negatively Curved Spaces
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Author : François Ledrappier
language : en
Publisher: American Mathematical Society
Release Date : 2023-01-18
The Regularity Of The Linear Drift In Negatively Curved Spaces written by François Ledrappier and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-01-18 with Mathematics categories.
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Lectures On Spaces Of Nonpositive Curvature
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Author : Werner Ballmann
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
Lectures On Spaces Of Nonpositive Curvature written by Werner Ballmann and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Singular spaces with upper curvature bounds and, in particular, spaces of nonpositive curvature, have been of interest in many fields, including geometric (and combinatorial) group theory, topology, dynamical systems and probability theory. In the first two chapters of the book, a concise introduction into these spaces is given, culminating in the Hadamard-Cartan theorem and the discussion of the ideal boundary at infinity for simply connected complete spaces of nonpositive curvature. In the third chapter, qualitative properties of the geodesic flow on geodesically complete spaces of nonpositive curvature are discussed, as are random walks on groups of isometries of nonpositively curved spaces. The main class of spaces considered should be precisely complementary to symmetric spaces of higher rank and Euclidean buildings of dimension at least two (Rank Rigidity conjecture). In the smooth case, this is known and is the content of the Rank Rigidity theorem. An updated version of the proof of the latter theorem (in the smooth case) is presented in Chapter IV of the book. This chapter contains also a short introduction into the geometry of the unit tangent bundle of a Riemannian manifold and the basic facts about the geodesic flow. In an appendix by Misha Brin, a self-contained and short proof of the ergodicity of the geodesic flow of a compact Riemannian manifold of negative curvature is given. The proof is elementary and should be accessible to the non-specialist. Some of the essential features and problems of the ergodic theory of smooth dynamical systems are discussed, and the appendix can serve as an introduction into this theory.
