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

1997/11/12 by Henning Schomerus
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Chaos control and synchronization #Quantum chaos and dynamical systems #chao-dyn #nlin.CD

paper · pdf · doi:10.1088/0305-4470/31/18/008

published as J. Phys. A: Math. Gen. 31 (1998) 4167-4196 · 18 pages RevTeX, 10 figures

arxiv created 1997/11/12 · openalex publication_date 1998/05/08 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30

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 formulae and determine also certain global bifurcations in conjunction with Stokes transitions that become important in the ensuing diffraction catastrophe integrals.

Citations

• Bifurcations of periodic orbits and uniform approximations
• Semiclassical interference of bifurcations
• Uniform approximation for period-quadrupling bifurcations

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