A group theoretical approach to hydrodynamics considers hydrodynamics to be the
differential geometry of diffeomorphism groups. The principle of least action implies that the …

Preface “... ad alcuno, dico, di quelli, che troppo laconicamente vorrebbero vedere, nei piu
angusti spazii che possibil fusse, ristretti i filosofici insegnamenti, sı che sempre si usasse …

It was recognized, since the seminal papers of Arnold (Ann Inst Grenoble 16: 319–361,
1966) and Ebin-Marsden (Ann Math Ser 2 92 (1): 102–163, 1970), that Euler's equations are …

Point-vortex dynamics describe idealized, non-smooth solutions to the incompressible Euler
equations on two-dimensional manifolds. Integrability results for few point-vortices on …

This work focuses on optimizing the displacement of a passive particle interacting with
vortices located on the surface of a sphere. The goal is to minimize the energy expended …

Isospectral flows are abundant in mathematical physics; the rigid body, the the Toda lattice,
the Brockett flow, the Heisenberg spin chain, and point vortex dynamics, to mention but a …

We investigate the dynamical system of point vortices on the hyperboloid. This system has
non-compact symmetry SL (2, R) and a coadjoint equivariant momentum map. The relative …

Vortex points on a sphere can be considered as simplified models of atmospheric
circulation. The use of these models allows the simulation of displacements of passive …

The objective of this study is to control the motion of a passive particle advected by N point
vortices in a sphere. The square of the L 2 norm of control, necessary for the system to …

This paper is concerned with the problem of three vortices on a sphere S 2 and the
Lobachevsky plane L 2. After reduction, the problem reduces in both cases to investigating a …