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On a class of integrable systems with a quartic first integral

On a class of integrable systems with a quartic first integral We generalize, to some extent, the results on integrable geodesic flows on two dimensional manifolds with a quartic first integral in the framework laid down by Selivanova and Hadeler. The local structure is first determined by a direct integration of the differential system which expresses the conservation of the quartic observable and is seen to involve a finite number of parameters. The global structure is studied in some detail and leads to a class of models on the manifolds {ie394-1}2, ℍ2 or ℝ2. As special cases we recover Kovalevskaya’s integrable system and a generalization of it due to Goryachev. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Regular and Chaotic Dynamics Springer Journals

On a class of integrable systems with a quartic first integral

Regular and Chaotic Dynamics , Volume 18 (4) – Aug 7, 2013

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References (13)

Publisher
Springer Journals
Copyright
Copyright © 2013 by Pleiades Publishing, Ltd.
Subject
Mathematics; Dynamical Systems and Ergodic Theory
ISSN
1560-3547
eISSN
1468-4845
DOI
10.1134/S1560354713040060
Publisher site
See Article on Publisher Site

Abstract

We generalize, to some extent, the results on integrable geodesic flows on two dimensional manifolds with a quartic first integral in the framework laid down by Selivanova and Hadeler. The local structure is first determined by a direct integration of the differential system which expresses the conservation of the quartic observable and is seen to involve a finite number of parameters. The global structure is studied in some detail and leads to a class of models on the manifolds {ie394-1}2, ℍ2 or ℝ2. As special cases we recover Kovalevskaya’s integrable system and a generalization of it due to Goryachev.

Journal

Regular and Chaotic DynamicsSpringer Journals

Published: Aug 7, 2013

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