Stability Properties of the Riemann Ellipsoids
Differential Geometry
2009-10-31 v1 Dynamical Systems
Symplectic Geometry
Abstract
We study the ellipticity and the ``Nekhoroshev stability'' (stability properties for finite, but very long, time scales) of the Riemann ellipsoids. We provide numerical evidence that the regions of ellipticity of the ellipsoids of types II and III are larger than those found by Chandrasekhar in the 60's and that all Riemann ellipsoids, except a finite number of codimension one subfamilies, are Nekhoroshev--stable. We base our analysis on a Hamiltonian formulation of the problem on a covering space, using recent results from Hamiltonian perturbation theory.
Cite
@article{arxiv.math/0002011,
title = {Stability Properties of the Riemann Ellipsoids},
author = {Francesco Fasso` and Debra Lewis},
journal= {arXiv preprint arXiv:math/0002011},
year = {2009}
}
Comments
29 pages, 6 figures