Authors:
The 1970 Moscow thesis of G. Margulis is published for the first time in English language
Complemented by a survey by R. Sharp, discussing more recent developments in the theory of periodic orbits and hyperbolic flows
Part of the book series: Springer Monographs in Mathematics (SMM)
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Table of contents (2 chapters)
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Front Matter
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Back Matter
About this book
In this book the seminal 1970 Moscow thesis of Grigoriy A. Margulis is published for the first time. Entitled "On Some Aspects of the Theory of Anosov Systems", it uses ergodic theoretic techniques to study the distribution of periodic orbits of Anosov flows. The thesis introduces the "Margulis measure" and uses it to obtain a precise asymptotic formula for counting periodic orbits. This has an immediate application to counting closed geodesics on negatively curved manifolds. The thesis also contains asymptotic formulas for the number of lattice points on universal coverings of compact manifolds of negative curvature.
The thesis is complemented by a survey by Richard Sharp, discussing more recent developments in the theory of periodic orbits for hyperbolic flows, including the results obtained in the light of Dolgopyat's breakthroughs on bounding transfer operators and rates of mixing.
Keywords
- Anosov Flows
- Hyperbolic Flows
- Lebesgue measures
- Periodic Orbits
- Riemannian Geometry
- dynamical systems
- ergodic theory
Authors and Affiliations
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Department of Mathematics, Yale University, New Haven, USA
Grigoriy A. Margulis
Bibliographic Information
Book Title: On Some Aspects of the Theory of Anosov Systems
Book Subtitle: With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows
Authors: Grigoriy A. Margulis
Series Title: Springer Monographs in Mathematics
DOI: https://doi.org/10.1007/978-3-662-09070-1
Publisher: Springer Berlin, Heidelberg
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eBook Packages: Springer Book Archive
Copyright Information: Springer-Verlag Berlin Heidelberg 2004
Hardcover ISBN: 978-3-540-40121-6Published: 03 December 2003
Softcover ISBN: 978-3-642-07264-2Published: 21 October 2010
eBook ISBN: 978-3-662-09070-1Published: 09 March 2013
Series ISSN: 1439-7382
Series E-ISSN: 2196-9922
Edition Number: 1
Number of Pages: VII, 144
Topics: Dynamical Systems, Geometry