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arXiv · math-ph/0211014

Non-Noether symmetries and their influence on phase space geometry

George Chavchanidze
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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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George Chavchanidze. 2003-07-09. Non-Noether symmetries and their influence on phase space geometry. https://doi.org/10.1016/s0393-0440(03)00040-8

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