Uniform approximation for period-quadrupling bifurcations
- 1 January 1998
- journal article
- Published by IOP Publishing in Journal of Physics A: General Physics
- Vol. 31 (1) , 165-183
- https://doi.org/10.1088/0305-4470/31/1/018
Abstract
We derive a uniform approximation for semiclassical contributions of periodic orbits to the spectral density which is valid for generic period-quadrupling bifurcations in systems with a mixed phase space. These bifurcations involve three periodic orbits which coalesce at the bifurcation. In the vicinity of the bifurcation the three orbits give a collective contribution to the spectral density while the individual contributions of Gutzwiller's type would diverge at the bifurcation. The uniform approximation is obtained by mapping the action function onto the normal form corresponding to the bifurcation. This article is a continuation of previous work in which uniform approximations for generic period-m-tupling bifurcations with were derived.Keywords
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This publication has 22 references indexed in Scilit:
- Semiclassical transition from an elliptical to an oval billiardJournal of Physics A: General Physics, 1997
- Bifurcations of periodic orbits and uniform approximationsJournal of Physics A: General Physics, 1997
- Uniform approximation for bifurcations of periodic orbits with high repetition numbersJournal of Physics A: General Physics, 1996
- Resonant periodic orbits and the semiclassical energy spectrumJournal of Physics A: General Physics, 1987
- Calculating the bound spectrum by path summation in action-angle variablesJournal of Physics A: General Physics, 1977
- Closed orbits and the regular bound spectrumProceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 1976
- Distribution of eigenfrequencies for the wave equation in a finite domain: III. Eigenfrequency density oscillationsAnnals of Physics, 1972
- Periodic Orbits and Classical Quantization ConditionsJournal of Mathematical Physics, 1971
- INSTABILITY IN A HAMILTONIAN SYSTEM AND THE DISTRIBUTION OF ASTEROIDSMathematics of the USSR-Sbornik, 1970
- Generic bifurcation of periodic pointsTransactions of the American Mathematical Society, 1970