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On Some Aspects of the Theory of Anosov Systems by Grigorii A. Margulis
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On Some Aspects of the Theory of Anosov Systems

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

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.
Release date Australia
October 21st, 2010
Audience
  • Professional & Vocational
Contributor
  • Commentaries by Richard Sharp
Edition
Softcover reprint of hardcover 1st ed. 2004
Illustrations
VII, 144 p.
Pages
144
Dimensions
156x234x8
ISBN-13
9783642072642
Product ID
8961323

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