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On Some Aspects of the Theory of Anosov Systems: With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows

On Some Aspects of the Theory of Anosov Systems: With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows

Hardcover

Series: Springer Monographs in Mathematics

General MathematicsGeometry

ISBN10: 3540401210
ISBN13: 9783540401216
Publisher: Springer
Published: Dec 3 2003
Pages: 144
Weight: 0.73
Height: 0.55 Width: 6.45 Depth: 9.43
Language: English

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. 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.

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Margulis, Grigorii A.

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General Mathematics