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

Medical Image Analysis

Research output: Contribution to journal › Article › Academic › peer-review

8 Citations (Scopus)

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

Access to Document

10.1134/S0012266115110087

Cite this

@article{29f179f80a724005956a24522e132965,

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).",

author = "A.P. Mashtakov and Sachkov, {Yu L.}",

year = "2015",

month = nov,

day = "1",

doi = "10.1134/S0012266115110087",

language = "English",

volume = "51",

pages = "1476--1483",

journal = "Differential Equations",

issn = "0012-2661",

publisher = "Maik Nauka-Interperiodica Publishing",

number = "11",

}

TY - JOUR

T1 - Superintegrability of left-invariant sub-Riemannian structures on unimodular three-dimensional Lie groups

AU - Mashtakov, A.P.

AU - Sachkov, Yu L.

PY - 2015/11/1

Y1 - 2015/11/1

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).

UR - http://www.scopus.com/inward/record.url?scp=84950236460&partnerID=8YFLogxK

U2 - 10.1134/S0012266115110087

DO - 10.1134/S0012266115110087

M3 - Article

AN - SCOPUS:84950236460

VL - 51

SP - 1476

EP - 1483

JO - Differential Equations

JF - Differential Equations

SN - 0012-2661

IS - 11

ER -

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

Abstract

Access to Document

Other files and links

Fingerprint

Cite this