Lambda-symmetries of Dynamical Systems, Hamiltonian and Lagrangian equations
arXiv:1102.3269
Abstract
After a brief survey of the definition and the properties of Lambda-symmetries in the general context of dynamical systems, the notion of "Lambda-constant of motion'' for Hamiltonian equations is introduced. If the Hamiltonian problem is derived from a Lambda-invariant Lagrangian, it is shown how the Lagrangian Lambda-invariance can be transferred into the Hamiltonian context and shown that the Hamiltonian equations turn out to be Lambda-symmetric. Finally, the "partial'' (Lagrangian) reduction of the Euler-Lagrange equations is compared with the reduction obtained for the corresponding Hamiltonian equations.
15 pages, Proceedings of Workshop on Group Analysis of Differential Equations and Integrable Systems, Protaras, Cyprus, June 2010