417 citations · 1.6k across the 72 of their papers we have counts for
4 papers · 1 filter
Linear stability in billiards with potential
Holger R. Dullin
A general formula for the linearized Poincaré map of a billiard with a potential is derived. The stability of periodic orbits is given by the trace of a product of matrices describ…
Elliptic Quantum Billiard
H. Waalkens, J. Wiersig, H. R. Dullin
The exact and semiclassical quantum mechanics of the elliptic billiard is investigated. The classical system is integrable and exhibits a separatrix, dividing the phasespace into r…
Inflation of Hamiltonian System: The Spinning Top in Projective Space
Holger R. Dullin
We present a method to enlarge the phase space of a canonical Hamiltonian System in order to remove coordinate singularities arising from a nontrivial topology of the configuration…
Topology of energy surfaces and existence of transversal Poincaré sections
Alexey Bolsinov, Holger R. Dullin, Andreas Wittek
Two questions on the topology of compact energy surfaces of natural two degrees of freedom Hamiltonian systems in a magnetic field are discussed. We show that the topology of this…