245 citations · 321 across the 8 of their papers we have counts for
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Normal Forms for Symplectic Maps with Twist Singularities
H. R. Dullin, A. V. Ivanov, J. D. Meiss
We derive a normal form for a near-integrable, four-dimensional symplectic map with a fold or cusp singularity in its frequency mapping. The normal form is obtained for when the fr…
Symbolic Codes for Rotational Orbits
Holger R. Dullin, James D. Meiss, David G. Sterling
Symbolic codes for rotational orbits and "islands-around-islands" are constructed for the quadratic, area-preserving Henon map. The codes are based upon continuation from an anti-i…
Vanishing Twist in the Hamiltonian Hopf Bifurcation
Holger R. Dullin, Alexey V. Ivanov
The Hamiltonian Hopf bifurcation has an integrable normal form that describes the passage of the eigenvalues of an equilibrium through the 1: -1 resonance. At the bifurcation the p…
(Vanishing) Twist in the Saddle-Centre and Period-Doubling Bifurcation
Holger R. Dullin, Alexey V. Ivanov
The lowest order resonant bifurcations of a periodic orbit of a Hamiltonian system with two degrees of freedom have frequency ratio 1:1 (saddle-centre) and 1:2 (period-doubling). T…
Generalizations of the Störmer Problem for Dust Grain Orbits
H. R. Dullin, M. Horányi, J. E. Howard
We consider the generalized Störmer Problem that includes the electromagnetic and gravitational forces on a charged dust grain near a planet. For dust grains a typical charge to ma…
About ergodicity in the family of limacon billiards
Holger R. Dullin, Arnd Bäcker
By continuation from the hyperbolic limit of the cardioid billiard we show that there is an abundance of bifurcations in the family of limacon billiards. The statistics of these bi…