46 citations · 258 across the 32 of their papers we have counts for
32 papers
Piecewise linear circle maps and conjugation to rigid rational rotations
Paul Glendinning, Siyuan Ma, James Montaldi
Criteria for piecewise linear circle homeomorphisms to be conjugate to a rigid rotation, , with rational rotation number are given. The consequences of…
A Hamiltonian approach for point vortices on non-orientable surfaces
Nataliya A. Balabanova, James Montaldi
We investigate the motion of point vortices on the Mobius band and Klein bottle. Since these are non-orientable surfaces, the standard Hamiltonian approach does not apply. We there…
Two body problem on a sphere in the presence of a uniform magnetic field
Nataliya A. Balabanova, James Montaldi
We investigate the motion of one and two charged non-relativistic particles on a sphere in the presence of a magnetic field of uniform strength. For one particle, the motion is alw…
Attracting and repelling 2-body problems on a family of surfaces of constant curvature
Luis García-Naranjo, James Montaldi
We first provide a classification of the pure rotational motion of 2 particles on a sphere interacting via a repelling potential. This is achieved by providing a simple geometric e…
Non-Abelian momentum polytopes for products of
James Montaldi, Amna Shaddad
This is the first of two companion papers. The joint aim is to study a generalization to higher dimension of the point vortex systems familiar in 2-D. In this paper we classify the…
Generalized point vortex dynamics on
James Montaldi, Amna Shaddad
This is the second of two companion papers. We describe a generalization of the point vortex system on surfaces to a Hamiltonian dynamical system consisting of two or three points…