Normal forms and uniform approximations for bridge orbit bifurcations
Chaotic Dynamics
2008-09-04 v3 Nuclear Theory
Abstract
We discuss various bifurcation problems in which two isolated periodic orbits exchange periodic ``bridge'' orbit(s) between two successive bifurcations. We propose normal forms which locally describe the corresponding fixed point scenarios on the Poincar\'e surface of section. Uniform approximations for the density of states for an integrable Hamiltonian system with two degrees of freedom are derived and successfully reproduce the numerical quantum-mechanical results.
Cite
@article{arxiv.0805.3755,
title = {Normal forms and uniform approximations for bridge orbit bifurcations},
author = {Ken-ichiro Arita and Matthias Brack},
journal= {arXiv preprint arXiv:0805.3755},
year = {2008}
}
Comments
25 pages, 18 figures, version published in Journal of Physics A: Mathematical and Theoretical