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Bifurcations of periodic orbits and uniform approximations.

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Bifurcations of periodic orbits and uniform approximations. / Schomerus, Henning; Sieber, Martin.
In: Journal of Physics A: Mathematical and General , Vol. 30, 1997, p. 4537.

Research output: Contribution to Journal/MagazineJournal articlepeer-review

Harvard

Schomerus, H & Sieber, M 1997, 'Bifurcations of periodic orbits and uniform approximations.', Journal of Physics A: Mathematical and General , vol. 30, pp. 4537. https://doi.org/10.1088/0305-4470/30/13/010

APA

Schomerus, H., & Sieber, M. (1997). Bifurcations of periodic orbits and uniform approximations. Journal of Physics A: Mathematical and General , 30, 4537. https://doi.org/10.1088/0305-4470/30/13/010

Vancouver

Schomerus H, Sieber M. Bifurcations of periodic orbits and uniform approximations. Journal of Physics A: Mathematical and General . 1997;30:4537. doi: 10.1088/0305-4470/30/13/010

Author

Schomerus, Henning ; Sieber, Martin. / Bifurcations of periodic orbits and uniform approximations. In: Journal of Physics A: Mathematical and General . 1997 ; Vol. 30. pp. 4537.

Bibtex

@article{b21f64a62eac4d4b989a9a964e0ddcf2,
title = "Bifurcations of periodic orbits and uniform approximations.",
abstract = "We derive uniform approximations for contributions to Gutzwiller's periodic-orbit sum for the spectral density which are valid close to bifurcations of periodic orbits in systems with mixed phase space. There, orbits lie close together and give collective contributions, while the individual contributions of Gutzwiller's type would diverge at the bifurcation. New results for the tangent, the period-doubling and the period-tripling bifurcation are given. They are obtained by going beyond the local approximation and including higher-order terms in the normal form of the action. The uniform approximations obtained are tested on the kicked top and are found to be in excellent agreement with exact quantum results.",
author = "Henning Schomerus and Martin Sieber",
year = "1997",
doi = "10.1088/0305-4470/30/13/010",
language = "English",
volume = "30",
pages = "4537",
journal = "Journal of Physics A: Mathematical and General ",
issn = "1361-6447",
publisher = "IOP Publishing Ltd",

}

RIS

TY - JOUR

T1 - Bifurcations of periodic orbits and uniform approximations.

AU - Schomerus, Henning

AU - Sieber, Martin

PY - 1997

Y1 - 1997

N2 - We derive uniform approximations for contributions to Gutzwiller's periodic-orbit sum for the spectral density which are valid close to bifurcations of periodic orbits in systems with mixed phase space. There, orbits lie close together and give collective contributions, while the individual contributions of Gutzwiller's type would diverge at the bifurcation. New results for the tangent, the period-doubling and the period-tripling bifurcation are given. They are obtained by going beyond the local approximation and including higher-order terms in the normal form of the action. The uniform approximations obtained are tested on the kicked top and are found to be in excellent agreement with exact quantum results.

AB - We derive uniform approximations for contributions to Gutzwiller's periodic-orbit sum for the spectral density which are valid close to bifurcations of periodic orbits in systems with mixed phase space. There, orbits lie close together and give collective contributions, while the individual contributions of Gutzwiller's type would diverge at the bifurcation. New results for the tangent, the period-doubling and the period-tripling bifurcation are given. They are obtained by going beyond the local approximation and including higher-order terms in the normal form of the action. The uniform approximations obtained are tested on the kicked top and are found to be in excellent agreement with exact quantum results.

U2 - 10.1088/0305-4470/30/13/010

DO - 10.1088/0305-4470/30/13/010

M3 - Journal article

VL - 30

SP - 4537

JO - Journal of Physics A: Mathematical and General

JF - Journal of Physics A: Mathematical and General

SN - 1361-6447

ER -