Canonical and canonoid transformations for Hamiltonian systems on (co)symplectic and (co)contact manifolds

Abstract

In this paper we present canonical and canonoid transformations considered as global geometrical objects for Hamiltonian systems. Under the mathematical formalisms of symplectic, cosymplectic, contact and cocontact geometry, the canonoid transformations are defined for (co)symplectic, (co)contact Hamiltonian systems, respectively. The local characterizations of these transformations is derived explicitly and it is demonstrated that for a given canonoid transformation there exist constants of motion associated with it

18 pages

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Cited by in corpus (3)

• Symmetries, conservation and dissipation in time-dependent contact systems
• The Herglotz variational principle for dissipative field theories
• Lie integrability by quadratures for symplectic, cosymplectic, contact and cocontact Hamiltonian systems