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Invariant measures of modified LR and L+R systems

Invariant measures of modified LR and L+R systems We introduce a class of dynamical systems having an invariant measure, the modifications of well-known systems on Lie groups: LR and L+R systems. As an example, we study a modified Veselova nonholonomic rigid body problem, considered as a dynamical system on the product of the Lie algebra so(n) with the Stiefel variety V n,r , as well as the associated єL+R system on so(n) × V n,r . In the 3-dimensional case, these systems model the nonholonomic problems of motion of a ball and a rubber ball over a fixed sphere. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Regular and Chaotic Dynamics Springer Journals

Invariant measures of modified LR and L+R systems

Regular and Chaotic Dynamics , Volume 20 (5) – Oct 16, 2015

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References (26)

Publisher
Springer Journals
Copyright
Copyright © 2015 by Pleiades Publishing, Ltd.
Subject
Mathematics; Dynamical Systems and Ergodic Theory
ISSN
1560-3547
eISSN
1468-4845
DOI
10.1134/S1560354715050032
Publisher site
See Article on Publisher Site

Abstract

We introduce a class of dynamical systems having an invariant measure, the modifications of well-known systems on Lie groups: LR and L+R systems. As an example, we study a modified Veselova nonholonomic rigid body problem, considered as a dynamical system on the product of the Lie algebra so(n) with the Stiefel variety V n,r , as well as the associated єL+R system on so(n) × V n,r . In the 3-dimensional case, these systems model the nonholonomic problems of motion of a ball and a rubber ball over a fixed sphere.

Journal

Regular and Chaotic DynamicsSpringer Journals

Published: Oct 16, 2015

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