Related Experiment Videos
Bifurcations in biparametric quadratic potentials. II.
1Departamento de Matematicas, Universidad de la Rioja, 26004 Logrono, SpainGrupo de Mecanica Espacial, Universidad de Zaragoza, 50009 Zaragoza, Spain.
Chaos (Woodbury, N.Y.)
|September 1, 1995
Summary
This study analyzes bifurcations in quadratic Hamiltonians on the S(2) sphere, identifying four key bifurcation types governing homoclinic orbits and system degeneracy.
Area of Science:
- Dynamical Systems
- Mathematical Physics
Background:
- Quadratic Hamiltonians on the S(2) sphere model diverse dynamical systems.
- Two primary classes of these Hamiltonians exist, each dependent on two parameters.
Purpose of the Study:
- To analyze bifurcations in one class of quadratic Hamiltonians on S(2).
- To map bifurcation lines in the parameter plane for this class.
- To complement prior research on the other class of Hamiltonians.
Main Methods:
- Analysis of quadratic Hamiltonians with phase space on the S(2) sphere.
- Identification and classification of bifurcation types.
- Mapping of bifurcation lines in the parameter plane.
Main Results:
- Four types of bifurcations (pitchfork, butterfly, oyster, pentadent) govern homoclinic orbit appearance/disappearance.
- Bifurcation lines were determined for one class of Hamiltonians.
- Degenerate system values with nonisolated equilibria were identified.
Conclusions:
- The study provides a comprehensive analysis of bifurcations for a specific class of quadratic Hamiltonians on S(2).
- The findings contribute to understanding the complex dynamics and phase space behavior of these systems.