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

Henning Schomerus

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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.


PACS

03.65.Sq Semiclassical theories and applications

05.45.Mt Quantum chaos; semiclassical methods

MSC

65P10 Hamiltonian systems including symplectic integrators

37G15 Bifurcations of limit cycles and periodic orbits

81Q20 Semiclassical techniques including WKB and Maslov methods

65P30 Bifurcation problems

Subjects

Statistical physics and nonlinear systems

Quantum information and quantum mechanics

Dates

Issue 18 (8 May 1998)

Received 12 November 1997, in final form 20 February 1998



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