Extensions of non-natural Hamiltonians

Abstract

The concept of extended Hamiltonian systems allows the geometrical interpretation of several integrable and superintegrable systems with polynomial first integrals of degree depending on a rational parameter. Until now, the procedure of extension has been applied only in the case of natural Hamiltonians. In this article, we give several examples of application to non-natural Hamiltonians, such as the two point-vortices, the Lotka-Volterra and some quartic in the momenta Hamiltonians, obtaining effectively extended Hamiltonians in some cases and failing in others. We briefly discuss the reasons of these results.

11 pages

References in corpus (5)

• The Tremblay-Turbiner-Winternitz system as extended Hamiltonian
• Extensions of Hamiltonian systems dependent on a rational parameter
• Superintegrable Extensions of Superintegrable Systems
• Extended Hamiltonians, Coupling-Constant Metamorphosis and the Post-Winternitz System
• Extended Hamiltonians and shift, ladder functions and operators