Periodic orbits near bifurcations of codimension two: Classical mechanics, semiclassics, and Stokes transitions

Abstract

We investigate classical and semiclassical aspects of codimension--two bifurcations of periodic orbits in Hamiltonian systems. A classification of these bifurcations in autonomous systems with two degrees of freedom or time-periodic systems with one degree of freedom is presented. We derive uniform approximations to be used in semiclassical trace formulas and determine also certain global bifurcations in conjunction with Stokes transitions that become important in the ensuing diffraction catastrophe integrals.

arXiv comment18 pages RevTeX, 10 figures

References in corpus (4)

• Bifurcations of Periodic Orbits and Uniform Approximations
• Uniform Approximation for Period-Quadrupling Bifurcations
• Semiclassical interference of bifurcations
• Semiclassical spectra from periodic-orbit clusters in a mixed phase space

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