Normal forms and uniform approximations for bridge orbit bifurcations

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 Poincaré 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.

25 pages, 18 figures, version published in Journal of Physics A: Mathematical and Theoretical

References in corpus (13)

• Bifurcations of Periodic Orbits and Uniform Approximations
• Semiclassical Transition from an Elliptical to an Oval Billiard
• Uniform Approximation for Period-Quadrupling Bifurcations
• Semiclassical interference of bifurcations
• Periodic orbits near bifurcations of codimension two: Classical mechanics, semiclassics, and Stokes transitions
• Semiclassical spectra from periodic-orbit clusters in a mixed phase space
• Uniform trace formulae for SU(2) and SO(3) symmetry breaking
• Uniform approximations for pitchfork bifurcation sequences
• On the canonically invariant calculation of Maslov indices
• Uniform semiclassical trace formula for U(3) --> SO(3) symmetry breaking
• Analytical perturbative approach to periodic orbits in the homogeneous quartic oscillator potential
• Transcritical bifurcations in non-integrable Hamiltonian systems
• Periodic-orbit bifurcations as the origin of nuclear deformations

Cited by in corpus (9)

• Shell structure and orbit bifurcations in finite fermion systems
• Periodic-orbit approach to the nuclear shell structures with power-law potential models: Bridge orbits and prolate-oblate asymmetry
• Semiclassical origin of anomalous shell effect for tetrahedral deformation in radial power-law potential model
• Semiclassical trace formula for the two-dimensional radial power-law potentials
• Semiclassical catastrophe theory of simple bifurcations
• The symmetric 1:2 resonance
• Shells, orbit bifurcations and symmetry restorations in Fermi systems
• Semiclassical approaches to nuclear dynamics
• Classical periodic orbits in extended phase space for spherical harmonic oscillator with spin-orbit coupling