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

A.P. Mashtakov; Yu L. Sachkov

doi:10.1134/S0012266115110087

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

A.P. Mashtakov, Yu L. Sachkov

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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).

Original language	English
Pages (from-to)	1476-1483
Number of pages	8
Journal	Differential Equations
Volume	51
Issue number	11
DOIs	https://doi.org/10.1134/S0012266115110087
Publication status	Published - 1 Nov 2015

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title = "Superintegrability of left-invariant sub-Riemannian structures on unimodular three-dimensional Lie groups",

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).",

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AU - Sachkov, Yu L.

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N2 - 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).

AB - 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).

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JO - Differential Equations

JF - Differential Equations

IS - 11

ER -

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

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