Non-Noether symmetries and their influence on phase space geometry

2002/11/30 by George Chavchanidze · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Homotopy and Cohomology in Algebraic Topology #Nonlinear Waves and Solitons #math-ph #math.MP #math.SG #msc:53Z05 #msc:70H06 #msc:70H33

paper · pdf · doi:10.1016/s0393-0440(03)00040-8

published as J. Geom. Phys. 48 (2003) 190-202 · LaTeX 2e article, 16 pages, no figures, revised version

openalex publication_date 2003/04/30 · arxiv created 2003/07/09 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We 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.

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• Non-Noether symmetries in integrable models

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