Bifurcation of resonances in a ring model
Abstract
Abstract We consider a particle in a ring system around a primary body, which is modeled as an ellipsoid. We study the occurrence of bifurcations associated to resonances, which arise at different values of the orbital eccentricity of the particle. The analysis of the bifurcations is first conducted by establishing theoretical conditions ensuring the existence of equilibria. Then, each specific resonance is examined through the study of the associated linearized system; their stability is obtained by computing the eigenvalues of the corresponding Jacobian matrix. Our results reveal a variety of dynamical behaviours characterizing the resonances, including pitchfork, saddle-node and transcritical bifurcations.
Fields of Study & Subjects
Advanced Differential Equations and Dynamical Systems
Quantum chaos and dynamical systems
Spectral Theory in Mathematical Physics
Publication details
- Journal / source
- Ricerche di Matematica
- Publisher
- Springer Science and Business Media LLC
- Volume
- 75
- Issue
- 4
- Pages
- 1887–1903
- Publication date
- 18 May 2026
- Language
- EN