Involutive orbits of non-Noether symmetry groups

Abstract

We consider set of functions on Poisson manifold related by continues one-parameter group of transformations. Class of vector fields that produce involutive families of functions is investigated and relationship between these vector fields and non-Noether symmetries of Hamiltonian dynamical systems is outlined. Theory is illustrated with sample models: modified Boussinesq system and Broer-Kaup system.

LaTeX 2e, 10 pages, no figures

References in corpus (3)

• Bihamiltonian Geometry, Darboux Coverings, and Linearization of the KP Hierarchy
• A simple way of making a Hamiltonian system into a bi-Hamiltonian one
• Non-Noether symmetries and their influence on phase space geometry