Fedotkin, Sergey N. and Magner, Alexander G. and Brack, Matthias (2008) Analytic approach to bifurcation cascades in a class of generalized Henon-Heiles potentials. PHYSICAL REVIEW E, 77 (6): 066219. ISSN 1539-3755,
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We investigate the bifurcation cascades of a linear librational orbit in a generalized class of Henon-Heiles potentials. The stability traces of the new orbits created at its bifurcations are found numerically to intersect linearly at the saddle energy (e=1), forming what we term the "Henon-Heiles fans." In the limit close to the saddle energy (e -> 1), where the dynamics is nearly chaotic, we derive analytical asymptotic expressions for the stability traces of both types of orbits and confirm the numerically determined properties of the generalized Henon-Heiles fans. As a bonus of our results, we obtain analytical approximations for the bifurcation energies e(n) which become asymptotically exact for e(n)-> 1.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | PERIODIC-ORBITS; QUANTUM BEATS; LEVEL DENSITY; SYSTEMS; SYMMETRY; BEHAVIOR; |
| Subjects: | 500 Science > 530 Physics |
| Divisions: | Physics > Institute of Theroretical Physics > Alumni or Retired Professors > Group Matthias Brack |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 02 Nov 2020 08:12 |
| Last Modified: | 02 Nov 2020 08:12 |
| URI: | https://pred.uni-regensburg.de/id/eprint/30859 |
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