On Some Aspects of the Theory of Anosov Systems With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows |
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| Author:
| Margulis, Grigorii A. |
| Commentaries by:
| Sharp, Richard |
| Series title: | Springer Monographs in Mathematics Ser. |
| ISBN: | 978-3-642-07264-2 |
| Publication Date: | Oct 2010 |
| Publisher: | Springer Berlin / Heidelberg
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| Imprint: | Springer |
| Book Format: | Paperback |
| List Price: | USD $54.99 |
Book Description:
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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...
More 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.