Martin Sieber and Henning Schomerus 1998 J. Phys. A: Math. Gen. 31 165 doi:10.1088/0305-4470/31/1/018
Uniform approximation for period-quadrupling bifurcations
Martin Sieber
and Henning Schomerus
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.
- PACS
- MSC
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81Q20 Semiclassical techniques including WKB and Maslov methods
- Subjects
- Dates
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Issue 1 (9 January 1998)
Received 26 August 1997
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Uniform approximation for period-quadrupling bifurcations
Martin Sieber and Henning Schomerus 1998 J. Phys. A: Math. Gen. 31 165
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