Geodesic Flows:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Boston, MA
Birkhäuser Boston
1999
|
| Schriftenreihe: | Progress in Mathematics
180 |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Beschreibung: | 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 |
| Beschreibung: | 1 Online-Ressource (XIII, 149 p) |
| ISBN: | 9781461216001 9781461272120 |
| DOI: | 10.1007/978-1-4612-1600-1 |
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| 500 | |a 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 | ||
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Datensatz im Suchindex
| _version_ | 1804153091042312192 |
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| author | Paternain, Gabriel P. |
| author_facet | Paternain, Gabriel P. |
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| dewey-full | 514.74 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
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| dewey-search | 514.74 |
| dewey-sort | 3514.74 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-1-4612-1600-1 |
| format | Electronic eBook |
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| id | DE-604.BV042419877 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:05Z |
| institution | BVB |
| isbn | 9781461216001 9781461272120 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027855294 |
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| physical | 1 Online-Ressource (XIII, 149 p) |
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| spelling | Paternain, Gabriel P. Verfasser aut Geodesic Flows by Gabriel P. Paternain Boston, MA Birkhäuser Boston 1999 1 Online-Ressource (XIII, 149 p) txt rdacontent c rdamedia cr rdacarrier Progress in Mathematics 180 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 Mathematics Differentiable dynamical systems Global analysis Topology Global Analysis and Analysis on Manifolds Dynamical Systems and Ergodic Theory Mathematik Geodätischer Fluss (DE-588)4156670-1 gnd rswk-swf Riemannscher Raum (DE-588)4128295-4 gnd rswk-swf Geodätischer Fluss (DE-588)4156670-1 s Riemannscher Raum (DE-588)4128295-4 s 1\p DE-604 https://doi.org/10.1007/978-1-4612-1600-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Paternain, Gabriel P. Geodesic Flows Mathematics Differentiable dynamical systems Global analysis Topology Global Analysis and Analysis on Manifolds Dynamical Systems and Ergodic Theory Mathematik Geodätischer Fluss (DE-588)4156670-1 gnd Riemannscher Raum (DE-588)4128295-4 gnd |
| subject_GND | (DE-588)4156670-1 (DE-588)4128295-4 |
| title | Geodesic Flows |
| title_auth | Geodesic Flows |
| title_exact_search | Geodesic Flows |
| title_full | Geodesic Flows by Gabriel P. Paternain |
| title_fullStr | Geodesic Flows by Gabriel P. Paternain |
| title_full_unstemmed | Geodesic Flows by Gabriel P. Paternain |
| title_short | Geodesic Flows |
| title_sort | geodesic flows |
| topic | Mathematics Differentiable dynamical systems Global analysis Topology Global Analysis and Analysis on Manifolds Dynamical Systems and Ergodic Theory Mathematik Geodätischer Fluss (DE-588)4156670-1 gnd Riemannscher Raum (DE-588)4128295-4 gnd |
| topic_facet | Mathematics Differentiable dynamical systems Global analysis Topology Global Analysis and Analysis on Manifolds Dynamical Systems and Ergodic Theory Mathematik Geodätischer Fluss Riemannscher Raum |
| url | https://doi.org/10.1007/978-1-4612-1600-1 |
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