INTEGRABLE GEODESIC FLOWS ON TWO-DIMENSIONAL SURFACES by A. V. Bolsinov, A. T. Fomenko ( 9780306110658 )

Item Details

Title:

INTEGRABLE GEODESIC FLOWS ON TWO-DIMENSIONAL SURFACES

By:

Format:

Hardback

List price:	£224.50
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ISBN 10:

0306110652

ISBN 13:

9780306110658

Publisher:

SPRINGER SCIENCE+BUSINESS MEDIA

Pub. date:

31 December, 1999

Edition:

2000 ed.

Series:

Monographs in Contemporary Mathematics

Pages:

322

Description:

Presents a different approach to qualitative analysis of integrable geodesic flows based on the theory of topological classification of integrable Hamiltonian systems. This book applies this technique systematically to a wide class of integrable systems. It features a systematic presentation of material on this subject, and contains illustrations.

Synopsis:

Geodesic flows of Riemannian metrics on manifolds are one of the classical objects in geometry. A particular place among them is occupied by integrable geodesic flows. We consider them in the context of the general theory of integrable Hamiltonian systems, and in particular, from the viewpoint of a new topological classification theory, which was recently developed for integrable Hamiltonian systems with two degrees of freedom. As a result, we will see that such a new approach is very useful for a deeper understanding of the topology and geometry of integrable geodesic flows. The main object to be studied in our paper is the class of integrable geodesic flows on two-dimensional surfaces. There are many such flows on surfaces of small genus, in particular, on the sphere and torus. On the contrary, on surfaces of genus 9 > 1, no such flows exist in the analytical case. One of the most important and interesting problems consists in the classification of integrable flows up to different equivalence relations such as (1) an isometry, (2) the Liouville equivalence, (3) the trajectory equivalence (smooth and continuous), and (4) the geodesic equivalence. In recent years, a new technique was developed, which gives, in particular, a possibility to classify integrable geodesic flows up to these kinds of equivalences. This technique is presented in our paper, together with various applications. The first part of our book, namely, Chaps.

Illustrations:

XIII, 322 p.

Publication:

Imprint:

Kluwer Academic/Plenum Publishers

Returns:

Returnable

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