4 papers
Birkhoff normal forms, Dirac brackets and symplectic reduction
Jose Lamas, Lei Zhao
Dirac brackets are widely used to study constrained Hamiltonian dynamics. In this paper we develop a Dirac-bracket approach to normal forms on momentum levels and relate it to symp…
Poncelet property of planar elliptic integrable Kepler billiards
Daniel Jaud, Lei Zhao
We consider the integrable dynamics of a Kepler billiard in the plane bounded by a branch of a conic section focused at the Kepler center. We show that in this case, for non-zero-e…
Integrability of Kepler Billiards at Zero-Energy
Lei Zhao
We consider a Kepler billiard with zero-energy in the plane defined inside a smooth closed connected simple curve which intersects all focused parabola at at most two points. {We s…
Geometric properties of integrable Kepler and Hooke billiards with conic section boundaries
Daniel Jaud, Lei Zhao
We study the geometry of reflection of a massive point-like particle at conic section boundaries. Thereby the particle is subjected to a central force associated with either a Kepl…