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18 - Integrability of the Sub-Riemannian Geodesic Flowon 3D Lie Groups

Published online by Cambridge University Press:  28 October 2019

Andrei Agrachev ,
Davide Barilari  and
Ugo Boscain
Andrei Agrachev
Affiliation:
Scuola Internazionale Superiore di Studi Avanzati, Trieste
Davide Barilari
Affiliation:
Université de Paris VII (Denis Diderot)
Ugo Boscain
Affiliation:
Centre National de la Recherche Scientifique (CNRS), Paris
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Summary

In this chapter we show how to find certain firstintegrals, for Hamiltonian systems on Lie groups,that are automatically in involution with each otherand with the Hamiltonian. This theory will be usedto prove that the Hamiltonian system for normalPontryagin extremals for rank-2 left-invariantsub-Riemannian structures on three-dimensional Liegroups is completely integrable.

Keywords

complete integrabilityPoisson manifoldsCasimir functions
Type
Chapter
Information
A Comprehensive Introduction to Sub-Riemannian Geometry , pp. 607 - 632
Publisher: Cambridge University Press
Print publication year: 2019

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