Abstract. We consider a set of functions on the Poisson manifold related by a continuous one-parameter group of transformations. A class of vector fields that produce involutive families of functions is investigated and the relationship between these vector fields and non-Noether symmetries of Hamiltonian dynamical systems is outlined. The theory is illustrated with two examples: a modified Boussinesq system and a Broer–Kaup system.

PACS numbers: 02.30.Ik, 11.30.Na, 45.20.Jj, 02.40.Hw

Mathematics Subject Classification: 70H33, 70H06, 58J70, 53Z05, 35A30

Print publication: Issue 29 (22 July 2005)
Received 20 April 2005, in final form 2 June 2005
Published 6 July 2005