Invariant measures for contact Hamiltonian systems: symplectic sandwiches with contact bread
A Bravetti, M de León, J C Marrero, E Padrón
Abstract
Abstract We prove that, under some natural conditions, Hamiltonian systems on a contact manifold C can be split into a Reeb dynamics on an open subset of C and a Liouville dynamics on a submanifold of C of codimension 1. For the Reeb dynamics we find an invariant measure. Moreover, we show that, under certain completeness conditions, the existence of an invariant measure for the Liouville dynamics can be characterized using the notion of a symplectic sandwich with contact bread.
Topics & Concepts
Symplectic geometryMathematicsSubmanifoldCodimensionInvariant (physics)Symplectic manifoldHamiltonian mechanicsPure mathematicsHamiltonian (control theory)Hamiltonian systemContact geometryMathematical analysisInvariant measureLagrangianSymplectomorphismManifold (fluid mechanics)Dynamical systems theoryMeasure (data warehouse)Mathematical physicsAbsolute continuityProbability measurePeriodic orbitsQuantum chaos and dynamical systemsControl and Stability of Dynamical SystemsGeometric and Algebraic Topology