TY - JOUR

T1 - Uniform approximation for period-quadrupling bifurcations.

AU - Sieber, Martin

AU - Schomerus, Henning

PY - 1998

Y1 - 1998

N2 - 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 m=/4 were derived.

AB - 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 m=/4 were derived.

U2 - 10.1088/0305-4470/31/1/018

DO - 10.1088/0305-4470/31/1/018

M3 - Journal article

VL - 31

SP - 165

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 1361-6447

ER -