Monographs in Contemporary Mathematics
cover

Integrable Geodesic Flows on Two-Dimensional Surfaces

Authors: Bolsinov, A.V., Fomenko, A.T.

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Hardcover 228,79 €
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  • ISBN 978-0-306-11065-8
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About this book

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.

Buy this book

Hardcover 228,79 €
price for Spain (gross)
  • ISBN 978-0-306-11065-8
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 187,19 €
price for Spain (gross)
  • ISBN 978-1-4613-6933-2
  • Free shipping for individuals worldwide
  • Institutional customers should get in touch with their account manager
  • Shipping restrictions
  • Usually ready to be dispatched within 3 to 5 business days, if in stock
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Integrable Geodesic Flows on Two-Dimensional Surfaces
Authors
Series Title
Monographs in Contemporary Mathematics
Copyright
2000
Publisher
Springer US
Copyright Holder
Springer Science+Business Media New York
Hardcover ISBN
978-0-306-11065-8
Softcover ISBN
978-1-4613-6933-2
Edition Number
1
Number of Pages
XIII, 322
Topics