M Sieber 1996 J. Phys. A: Math. Gen. 29 4715 doi:10.1088/0305-4470/29/15/034
Uniform approximation for bifurcations of periodic orbits with high repetition numbers
M Sieber
Show affiliationsThe semiclassical contribution of a periodic orbit to the quantum density of states diverges when the orbit bifurcates. In this case one has to apply approximations which are uniformly valid both in 
and a parameter 
which describes the distance to the bifurcation. The form of the approximation depends on the repetition number m of the orbit that bifurcates. In a two-dimensional system, the approximations are different for m = 1 up to m = 5, and for 
they have the same form as for m = 5. In this article, we consider the case which occurs first when an integrable system is perturbed. A uniform approximation for the contribution to the spectral density is derived, which in the limit of large reduces to a sum of semiclassical contributions of isolated periodic orbits.
- PACS
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05.45.Mt Quantum chaos; semiclassical methods
02.30.Mv Approximations and expansions
- MSC
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81Q50 Quantum chaos (See also 37Dxx)
81Q20 Semiclassical techniques including WKB and Maslov methods
37G15 Bifurcations of limit cycles and periodic orbits
37Mxx Approximation methods and numerical treatment of dynamical systems (See also 65Pxx)
- Subjects
- Dates
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Issue 15 (7 August 1996)
Received 9 February 1996, in final form 17 May 1996
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Uniform approximation for bifurcations of periodic orbits with high repetition numbers
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