On some aspects of the theory of Anosov systems : with a survey by Richard Sharp, periodic orbits of hyperbolic flows
Author(s)
Bibliographic Information
On some aspects of the theory of Anosov systems : with a survey by Richard Sharp, periodic orbits of hyperbolic flows
（Springer monographs in mathematics）
Springer, c2004
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Library, Research Institute for Mathematical Sciences, Kyoto University数研
MAR||80||2(V)03065051
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Note
Includes bibliographical references(p.[70]-71, [133]-138) and index
Translated from the Russian by Szulikowska Valentina Vladimirovna
Contents of Works
- Periodic orbits of hyperbolic flows / Richard Sharp
Description and Table of Contents
Description
The seminal 1970 Moscow thesis of Grigoriy A. Margulis, 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.
Table of Contents
On Some Aspects of the Theory of Anosov Systems.- Periodic Orbits of Hyperbolic Flows.
by "Nielsen BookData"