Bifurcations of Riemann Ellipsoids
Abstract
Abstract. We give an account of the various changes in the stability character of three types of Riemann ellipsoids by establishing the occurrence of different quasi-periodic Hamiltonian bifurcations. Suitable symplectic changes of coordinates, that is, linear and nonlinear normal form transformations are performed, leading to the characterization of the bifurcations responsible for the stability changes. Specifically we find three types of bifurcations, namely, Hamiltonian pitchfork, saddle-center, and Hamiltonian–Hopf in the four-degree-of-freedom Hamiltonian system resulting after reducing out the symmetries of the problem. The approach is mainly analytical up to a point where nondegeneracy conditions have to be checked numerically.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Quantum chaos and dynamical systems
Nonlinear Waves and Solitons
Publication details
- Journal / source
- SIAM Journal on Applied Dynamical Systems
- Volume
- 25
- Issue
- 2
- Pages
- 998–1041
- Publication date
- 27 April 2026
- Language
- EN