Non-Noether symmetries and their influence on phase space geometry

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dc.creatorChavchanidze, George
dc.date2002-11-09
dc.date2003-07-09
dc.date.accessioned2026-07-07T04:29:33Z
dc.date.available2026-07-07T04:29:33Z
dc.descriptionWe disscuss some geometric aspects of the concept of non-Noether symmetry. It is shown that in regular Hamiltonian systems such a symmetry canonically leads to a Lax pair on the algebra of linear operators on cotangent bundle over the phase space. Correspondence between the non-Noether symmetries and other wide spread geometric methods of generating conservation laws such as bi-Hamiltonian formalism, bidifferential calculi and Frolicher-Nijenhuis geometry is considered. It is proved that the integrals of motion associated with the continuous non-Noether symmetry are in involution whenever the generator of the symmetry satisfies a certain Yang-Baxter type equation.
dc.descriptionLaTeX 2e article, 16 pages, no figures, revised version
dc.identifierhttps://arxiv.org/abs/math-ph/0211014
dc.identifierhttp://arxiv.org/abs/math-ph/0211014
dc.identifierJ. Geom. Phys. 48 (2003) 190-202
dc.identifierdoi:10.1016/S0393-0440(03)00040-8
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57200
dc.subjectMathematical Physics
dc.subjectSymplectic Geometry
dc.subject70H33, 70H06, 53Z05
dc.titleNon-Noether symmetries and their influence on phase space geometry
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