417 citations · 1.6k across the 72 of their papers we have counts for
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Symmetry Reduction by Lifting for Maps
H. R. Dullin, H. E. Lomeli, J. D. Meiss
We study diffeomorphisms that have one-parameter families of continuous symmetries. For general maps, in contrast to the symplectic case, existence of a symmetry no longer implies…
Resonances and Twist in Volume-Preserving Mappings
H. R. Dullin, J. D. Meiss
The phase space of an integrable, volume-preserving map with one action and angles is foliated by a one-parameter family of -dimensional invariant tori. Perturbations of suc…
Quadratic Volume-Preserving Maps: Invariant Circles and Bifurcations
Holger R. Dullin, James D. Meiss
We study the dynamics of the five-parameter quadratic family of volume-preserving diffeomorphisms of R^3. This family is the unfolded normal form for a bifurcation of a fixed point…
A Poincaré section for the general heavy rigid body
Sven Schmidt, Holger R. Dullin, Peter H. Richter
A general recipe is developed for the study of rigid body dynamics in terms of Poincaré surfaces of section. A section condition is chosen which captures every trajectory on a give…
Nilpotent normal form for divergence-free vector fields and volume-preserving maps
H. R. Dullin, J. D. Meiss
We study the normal forms for incompressible flows and maps in the neighborhood of an equilibrium or fixed point with a triple eigenvalue. We prove that when a divergence free vect…
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…
Extended phase diagram of the Lorenz model
Holger R. Dullin, Sven Schmidt, Peter H. Richter +1
The parameter dependence of the various attractive solutions of the three variable nonlinear Lorenz model equations for thermal convection in Rayleigh-Bénard flow is studied. Its b…
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…
An Integrable Shallow Water Equation with Linear and Nonlinear Dispersion
Holger R. Dullin, Georg Gottwald, Darryl D. Holm
We study a class of 1+1 quadratically nonlinear water wave equations that combines the linear dispersion of the Korteweg-deVries (KdV) equation with the nonlinear/nonlocal dispersi…
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…