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On Some Aspects of the Theory of Anosov Systems

With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows

  • Book
  • © 2004

Overview

Authors:
  1. Grigoriy A. Margulis

    1. Department of Mathematics, Yale University, New Haven, USA

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  • 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)

  1. Front Matter

    Pages i-vii
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  2. On Some Aspects of the Theory of Anosov Systems

    • G. A. Margulis
    Pages 1-71

  3. Periodic Orbits of Hyperbolic Flows

    • Richard Sharp
    Pages 73-138

  4. Back Matter

    Pages 139-142
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Keywords

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.

Authors and Affiliations

  • 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

  • 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 and Ergodic Theory, Geometry

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