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Non-Noether symmetries in singular dynamical systems

George Chavchanidze
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Abstract

It's well known that Noether symmetries lead to the conservation laws. Conserved quantities are constructed out of generator of the symmetry - invariant Hamiltonian vector field. Considering more general class of vector fields - non-Hamiltonian ones leads to the notion of non-Noether symmetry and conservation laws (Lutzky's integrals of motion) with interesting properties. In the present paper correspondence between non-Noether symmetries and conserved quantities in different types of dynamical systems (DS on symplectic, presymplectic and Poisson manifolds) is considered.

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George Chavchanidze. 2001-06-15. Non-Noether symmetries in singular dynamical systems. https://arxiv.org/abs/math-ph/0106010

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