Berlin 2005 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 34: Poster

DY 34.39: Poster

Montag, 7. März 2005, 15:30–18:00, Poster TU D

Localisation At Resonance — •Oliver Strebel — Handjerystr. 31, 12159 Berlin

In nonlinear Hamiltonian systems with two degrees of freedom resonances occur, when the frequencies of the constituting subsystems are integer multiples of each other. In perturbation theories this circumstance gives rise to the famous small denominators of Poincare [1]. At resonance however averaging methods yield reasonable results [2].
In this contribution numerical data are studied at resonance in position coordinates and are compared to analytical approximations. They show a clear localisation of the trajectory in the sense that the trajectory covers only a small fraction of the position coordinates, which are accessible under the restriction of energy conservation. Shifting away from resonance more and more position coordinates are reached by the trajectory. The results are discussed within the framework of the Poincare-Birkhoff theorem [1].

A.J. Lichtenberg and M.A. Lieberman, Regular and chaotic dynamics, 2nd ed., Springer Berlin AMS 38 (1992).
V.M. Volosov, Russ. Math. Surveys, 17, 1, (1963).