Regensburg 2000 – wissenschaftliches Programm

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DY: Dynamik und Statistische Physik

DY 46: POSTER II

DY 46.42: Poster

Donnerstag, 30. März 2000, 15:00–18:00, D

Nonlinear Dynamical Systems close to Resonance — •Oliver Strebel — Handjerystr. 31, 12159 Berlin

Coupled nonlinear oscillators show quite complex behaviour, if the frequencies of the uncoupled constituent subsystems meet a so called resonance relation. For Hamiltonian systems it was shown (1) that far enough from resonances the invariant tori of the uncoupled systems persist for sufficient small perturbations, while large excursions of the action integral are possible close to resonance. Using several approximation schemes analytical trajectories for coupled or driven systems close to resonance are calculated and compared to numerical solutions. The connection between nonlinear resonances and the recently discovered phenomenon of measure synchronisation (2) is also discussed.
(1) V.I. Arnold, V.V. Kozlov, A.I. Neishtadt, Mathematical Aspects of Classical Mechanics (2. ed.), Springer Berlin (1997).
(2) A. Hampton, D. H. Zanette, Phys. Rev. Lett. 83, 2179, (1999).