Simple non-Hamiltonian systems with an invariant measure

Abstract

We propose a simple construction of the non-Hamiltonian dynamical systems possessing an invariant measure. These non-Hamiltonian systems are deformations of the Hamiltonian systems associated with trivial deformations of the canonical Poisson brackets and time transformation. Sometimes these non-Hamiltonian systems can be identified with known nonholonomic systems and, therefore, the results are illustrated through the Chaplygin ball and the Veselova system.

14 pages, LaTeX with AMS fonts

References in corpus (4)

• Nonholonomic Hamilton-Jacobi Theory via Chaplygin Hamiltonization
• Integrable Euler top and nonholonomic Chaplygin ball
• Canonical transformations of the extended phase space, Toda lattices and Stackel family of integrable systems
• Chaplygin systems associated to Cartan decompositions of semi-simple Lie algebras

Cited by in corpus (3)

• Integrability of Nonholonomic Heisenberg Type Systems
• On Integrable Perturbations of Some Nonholonomic Systems
• On generalized nonholonomic Chaplygin sphere problem