Isoenergetic Manifolds of Integrable Billiard Books
И. С. Харчева
Abstract
We consider a class of integrable Hamiltonian systems with two degrees of freedom, i.e., billiard books, which are a generalization of billiard in domains bounded by arcs of confocal quadrics. When studying billiard, first of all, the question arises about the topology of the phase space and the isoenergetic manifold. We prove that the phase space and the isoenergetic manifold in the case of billiard books are actually piecewise smooth manifolds.
Topics & Concepts
Dynamical billiardsIntegrable systemMathematicsPhase spacePure mathematicsManifold (fluid mechanics)Hamiltonian systemBounded functionGeneralizationMathematical analysisSpace (punctuation)PiecewiseGeometryPhysicsComputer scienceThermodynamicsOperating systemEngineeringMechanical engineeringQuantum chaos and dynamical systemsMathematical Dynamics and FractalsScientific Research and Discoveries