We generalize the Weinstein-Moser theorem on the existence of nonlinear normal modes near an equilibrium in a Hamiltonian system to a theorem on the existence of relative periodic orbits near aâ€¦ (More)

We prove that for every proper Hamiltonian action of a Lie group G in finite dimensions the momentum map is locally G-open relative to its image (i.e. images of G-invariant open sets are open). As anâ€¦ (More)

Point vortices on a cylinder (periodic strip) are studied geometrically. The Hamiltonian formalism is developed, a nonexistence theorem for relative equilibria is proved, equilibria are classifiedâ€¦ (More)

The locomotion of a body through an inviscid incompressible fluid, such that the flow remains irrotational everywhere, is known to depend on inertial forces and on both the shape and the massâ€¦ (More)

Proceedings of the National Academy of Sciencesâ€¦

1997

Capacity is an important numerical invariant of symplectic manifolds. This paper studies when a subset of a symplectic manifold is null, i.e., can be removed without affecting the ambient capacity.â€¦ (More)

A perpetual motion machine driven by buoyancy is presented. We see that it does not quite work, and we also discuss how it would move in reality. Debunking the trick behind most such machines is aâ€¦ (More)

Dynamics of point vortices is generalized in two ways: first by making the strengths complex, which allows for sources and sinks in superposition with the usual vortices, second by making themâ€¦ (More)