Contact Hamiltonian Systems

Abstract

In this paper we study Hamiltonian systems on contact manifolds, which is an appropriate scenario to discuss dissipative systems. We prove a coisotropic reduction theorem similar to the one in symplectic mechanics.

References in corpus (8)

• A survey on cosymplectic geometry
• Cosymplectic and contact structures to resolve time-dependent and dissipative hamiltonian systems
• New integrable (3+1)-dimensional systems and contact geometry
• A thermostat algorithm generating target ensembles
• Liouville's Theorem and the canonical measure for nonconservative systems from contact geometry
• Completely Integrable Contact Hamiltonian Systems and Toric Contact Structures on $S^2\times S^3$
• Quasi-morphisms on contactomorphism groups and contact rigidity
• Rigidity of integral coisotropic submanifolds of contact manifolds

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