Non-Noether symmetries and their influence on phase space geometry

Details Non-Noether symmetries and their influence on phase space geometry Non-Noether symmetries and their influence on phase space geometry

2002-11-09

arxiv.org/abs/math-ph/0211014v2

J. Geom. Phys. 48 (2003) 190-202

Physics

Mathematical Physics

LaTeX 2e article, 16 pages, no figures, revised version

Scientific paper

10.1016/S0393-0440(03)00040-8

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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