عنوان

On Some Aspects of the Theory of Anosov Systems :

(Number (ISBN

3662090708

(Number (ISBN

9783662090701

Number

b566987

Title Proper

On Some Aspects of the Theory of Anosov Systems :

General Material Designation

[Book]

Other Title Information

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

First Statement of Responsibility

by Grigoriy A. Margulis.

Place of Publication, Distribution, etc.

Berlin, Heidelberg

Name of Publisher, Distributor, etc.

Springer Berlin Heidelberg

Date of Publication, Distribution, etc.

2004

Specific Material Designation and Extent of Item

(vii, 142 pages)

Series Title

Springer monographs in mathematics.

Text of Note

G. Margulis: On Some Aspects of the Theory of Anosov Systems: 1. Some Preliminaries on Anosov Flows --; 2. Behaviour of Lebesgue Measures on Leaves of ~

Text of Note

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.

Differentiable dynamical systems.

Geometry.

Mathematics.

Class number

Book number

by Grigoriy A. Margulis.

Grigoriy A Margulis

Electronic name

[Book]

Y