Journal of Nonlinear Mathematical Physics

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Volume 18, Issue 2, June 2011, Pages 245 - 268

On bi-Integrable Natural Hamiltonian Systems on Riemannian Manifolds

Authors
A. V. Tsiganov
Department of Computational Physics, St. Petersburg State University, Ulyanovskaya, 3, St. Petersburg, 198504, Russian Federation,andrey.tsiganov@gmail.com
Received 3 June 2010, Accepted 25 October 2010, Available Online 7 January 2021.
DOI
10.1142/S1402925111001507How to use a DOI?
Keywords
Integrable system; Riemannian manifold; bi-hamiltonian geometry
Abstract

We introduce the concept of natural Poisson bivectors, which generalizes the Benenti approach to construction of natural integrable systems on Riemannian manifolds and allows us to consider almost the whole known zoo of integrable systems in framework of bi-hamiltonian geometry.

Copyright
© 2011 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
18 - 2
Pages
245 - 268
Publication Date
2021/01/07
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1142/S1402925111001507How to use a DOI?
Copyright
© 2011 The Authors. Published by Atlantis Press and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

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TY  - JOUR
AU  - A. V. Tsiganov
PY  - 2021
DA  - 2021/01/07
TI  - On bi-Integrable Natural Hamiltonian Systems on Riemannian Manifolds
JO  - Journal of Nonlinear Mathematical Physics
SP  - 245
EP  - 268
VL  - 18
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1142/S1402925111001507
DO  - 10.1142/S1402925111001507
ID  - Tsiganov2021
ER  -