Non-Noether symmetries in singular dynamical systems

Details Non-Noether symmetries in singular dynamical systems Non-Noether symmetries in singular dynamical systems

2001-06-15

arxiv.org/abs/math-ph/0106010v3

Georgian Math. J. 8 027-032 (2001)

Physics

Mathematical Physics

LaTeX 2e, 6 pages, no figures

Scientific paper

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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