Contact flows and integrable systems

Abstract

We consider Hamiltonian systems restricted to the hypersurfaces of contact type and obtain a partial version of the Arnold-Liouville theorem: the system not need to be integrable on the whole phase space, while the invariant hypersurface is foliated on an invariant Lagrangian tori. In the second part of the paper we consider contact systems with constraints. As an example, the Reeb flows on Brieskorn manifolds are considered.

25 pages, to appear in Journal of Geometry and Physics

References in corpus (7)

• The contact geometry of the restricted 3-body problem
• Torus Actions and Integrable Systems
• Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on $S^2\times S^3$
• Systems of Hess-Appel'rot type
• Heisenberg model in pseudo-Euclidean spaces
• The rigid body dynamics: classical and algebro-geometric integration
• Partial Reductions of Hamiltonian Flows and Hess-Appel'rot Systems on SO(n)

Cited by in corpus (12)

• Infinitesimal symmetries in Contact Hamiltonian systems
• Contact variational integrators
• A review on contact Hamiltonian and Lagrangian systems
• Extended Hamilton-Jacobi theory, contact manifolds and integrability by quadratures
• Noether symmetries and integrability in time-dependent Hamiltonian mechanics
• Heisenberg model in pseudo-Euclidean spaces
• Integrable systems in cosymplectic geometry
• Heisenberg model in pseudo-Euclidean spaces II
• Liouville-Arnold theorem for homogeneous symplectic and contact Hamiltonian systems
• Bott-integrable Reeb flows on 3-manifolds
• Contact line bundles, foliations, and integrability
• Generalized action-angle coordinates in toric contact spaces