11 citations · 17 across the 2 of their papers we have counts for
4 papers
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…
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…