Brack, Matthias and Mehta, M. and Tanaka, K. (2001) Occurrence of periodic Lame functions at bifurcations in chaotic Hamiltonian systems. JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 34 (40). pp. 8199-8220. ISSN 0305-4470
Full text not available from this repository.Abstract
We investigate cascades of isochronous pitchfork bifurcations of straight-line librating orbits in some two-dimensional Hamiltonian systems with mixed phase space. We show that the new bifurcated orbits, which are responsible for the onset of chaos, are given analytically by the periodic solutions of the Lame equation as classified in 1940 by Ince. In Hamiltonians with C-2v symmetry, they occur alternatingly as Lame functions of period 2K and 4K, respectively, where 4K is the period of the Jacobi elliptic function appearing in the Lame equation. We also show that the two pairs of orbits created at period-doubling bifurcations of island-chain type are given by two different linear combinations of algebraic Lame functions with period 8K.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | QUANTUM BEATS; LEVEL-DENSITY; ORBITS; UNIVERSALITY; QUANTIZATION; |
| 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: | 06 Dec 2021 07:16 |
| Last Modified: | 06 Dec 2021 07:16 |
| URI: | https://pred.uni-regensburg.de/id/eprint/41037 |
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