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Non-Hamiltonian systems separable by Hamilton-Jacobi method
Linköping University, The Institute of Technology. Linköping University, Department of Science and Technology.
Insitution för fysik Adam Mickiewicz universitet, Poznan, Poland.
2008 (English)In: Journal of Geometry and Physics, ISSN 0393-0440, Vol. 58, no 5, 557-575 p.Article in journal (Refereed) Published
Abstract [en]

We show that with every separable classical Stäckel system of Benenti type on a Riemannian space one can associate, by a proper deformation of the metric tensor, a multi-parameter family of non-Hamiltonian systems on the same space, sharing the same trajectories and related to the seed system by appropriate reciprocal transformations. These systems are known as bi-cofactor systems and are integrable in quadratures as the seed Hamiltonian system is. We show that with each class of bi-cofactor systems a pair of separation curves can be related. We also investigate the conditions under which a given flat bi-cofactor system can be deformed to a family of geodesically equivalent flat bi-cofactor systems. © 2007 Elsevier Ltd. All rights reserved.

Place, publisher, year, edition, pages
2008. Vol. 58, no 5, 557-575 p.
Keyword [en]
separability, Stäckel systems, bicofactor systems, separation curves
National Category
Engineering and Technology
URN: urn:nbn:se:liu:diva-40802DOI: 10.1016/j.geomphys.2007.12.008Local ID: 54152OAI: diva2:261651
Available from: 2009-10-10 Created: 2009-10-10 Last updated: 2011-01-10

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Marciniak, Krzysztof
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The Institute of TechnologyDepartment of Science and Technology
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