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Differential Equations

, Volume 51, Issue 11, pp 1476–1483 | Cite as

Superintegrability of left-invariant sub-Riemannian structures on unimodular three-dimensional Lie groups

Control Theory

Abstract

We consider left-invariant sub-Riemannian problems on three-dimensional unimodular Lie groups. We show that the Hamiltonian system of the Pontryagin maximum principle for such problems is Liouville integrable and even superintegrable (i.e., has four independent integrals, three of which are in involution).

Keywords

Hamiltonian System Hamiltonian Vector Pontryagin Maximum Principle Casimir Function Liouville Integrability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Pleiades Publishing, Ltd. 2015

Authors and Affiliations

  1. 1.Eindhoven University of TechnologyEindhovenNetherlands
  2. 2.University of Hradec KrálovéHradec KrálovéCzech Republic

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