245 citations · 321 across the 8 of their papers we have counts for
13 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…
Maslov Indices and Monodromy
HR Dullin, JM Robbins, H Waalkens +2
We prove that for a Hamiltonian system on a cotangent bundle that is Liouville-integrable and has monodromy the vector of Maslov indices is an eigenvector of the monodromy matrix w…
Spectra of Sol-manifolds: arithmetic and quantum monodromy
A. V. Bolsinov, H. R. Dullin, A. P. Veselov
The spectral problem of three-dimensional manifolds M_A admitting Sol-geometry in Thurston's sense is investigated. Topologically M_A are torus bundles over a circle with a unimodu…
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…
On asymptotically equivalent shallow water wave equations
H. R. Dullin, G. A. Gottwald, D. D. Holm
The integrable 3rd-order Korteweg-de Vries (KdV) equation emerges uniquely at linear order in the asymptotic expansion for unidirectional shallow water waves. However, at quadratic…
Vanishing Twist near Focus-Focus Points
Holger R. Dullin, Vu Ngoc San
We show that near a focus-focus point in a Liouville integrable Hamiltonian system with two degrees of freedom lines of locally constant rotation number in the image of the energy-…