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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. 117,69 €
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Technische Daten
Erscheinungsdatum
10.10.2012
Sprache
Englisch
EAN
9781461272120
Herausgeber
Birkhäuser Boston
Serien- oder Bandtitel
Progress in Mathematics
Sonderedition
Nein
Autor
Gabriel P. Paternain
Seitenanzahl
149
Einbandart
Broschiert
Schlagwörter
Fundamental group, Loop group, Riemannian manifold, curvature, differential geometry, dynamical systems, ergodic theory, homology, manifold
Thema-Inhalt
PBMP - Differentielle und Riemannsche Geometrie
PBK - Mathematische Analysis, allgemein
PBP - Topologie
GPFC - Kybernetik und Systemtheorie
Höhe
235 mm
Breite
15.5 cm
Transparenz & Sicherheit
Hersteller: Birkhäuser, Europaplatz 3, Heidelberg, Deutschland, 69115, ProductSafety@springernature.com, Springer Nature Customer Service Center GmbH
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