Springer Monographs in Mathematics: With a Survey by Richard Sharp: Periodic Orbits of Hyperbolic Flows

Margulis, Grigorii A.; Sharp, Richard

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.

Details

Published by: Springer

Publication Date: 2003-12-03

Format: Hardcover

ISBN-13: 9783540401216

DOI: 10.1007/978-3-662-09070-1

Dimensions: 235cm x155cm

Pages: 144