417 citations · 1.6k across the 72 of their papers we have counts for
8 papers · 1 filter
Homoclinic Bifurcations for the Henon Map
D. G. Sterling, H. R. Dullin, J. D. Meiss
Chaotic dynamics can be effectively studied by continuation from an anti-integrable limit. We use this limit to assign global symbols to orbits and use continuation from the limit…
Generic Twistless Bifurcations
H. R. Dullin, J. D. Meiss, D. Sterling
We show that in the neighborhood of the tripling bifurcation of a periodic orbit of a Hamiltonian flow or of a fixed point of an area preserving map, there is generically a bifurca…
Triaxial Ellipsoidal Quantum Billiards
Holger Waalkens, Jan Wiersig, Holger R. Dullin
The classical mechanics, exact quantum mechanics and semiclassical quantum mechanics of the billiard in the triaxial ellipsoid is investigated. The system is separable in ellipsoid…
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…
Symbolic Dynamics and Periodic Orbits for the Cardioid Billiard
A. Bäcker, H. R. Dullin
The periodic orbits of the strongly chaotic cardioid billiard are studied by introducing a binary symbolic dynamics. The corresponding partition is mapped to a topological well-ord…