Uniform approximations for pitchfork bifurcation sequences
Kaidel, J. ; Brack, M.
arXiv, 0308026 / Harvested from arXiv
Text on arXiv
In non-integrable Hamiltonian systems with mixed phase space and discrete symmetries, sequences of pitchfork bifurcations of periodic orbits pave the way from integrability to chaos. In extending the semiclassical trace formula for the spectral density, we develop a uniform approximation for the combined contribution of pitchfork bifurcation pairs. For a two-dimensional double-well potential and the familiar H\'enon-Heiles potential, we obtain very good agreement with exact quantum-mechanical calculations. We also consider the integrable limit of the scenario which corresponds to the bifurcation of a torus from an isolated periodic orbit. For the separable version of the H\'enon-Heiles system we give an analytical uniform trace formula, which also yields the correct harmonic-oscillator SU(2) limit at low energies, and obtain excellent agreement with the slightly coarse-grained quantum-mechanical density of states.
Publié le : 2003-08-25
Classification:  Nonlinear Sciences - Chaotic Dynamics,  Mathematical Physics,  Nonlinear Sciences - Exactly Solvable and Integrable Systems 
@article{0308026,
     author = {Kaidel, J. and Brack, M.},
     title = {Uniform approximations for pitchfork bifurcation sequences},
     journal = {arXiv},
     volume = {2003},
     number = {0},
     year = {2003},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0308026}
}

Kaidel, J.; Brack, M. Uniform approximations for pitchfork bifurcation sequences. arXiv, Tome 2003 (2003) no. 0, . http://gdmltest.u-ga.fr/item/0308026/