Chaotic Scattering in Time-Dependent Hamiltonian Systems

Ying-Cheng Lai*, Celso Grebogi

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We consider the classical scattering of particles in a one-degree-of-freedom, time-dependent Hamiltonian system. We demonstrate that chaotic scattering can be induced by periodic oscillations in the position of the potential. We study the invariant sets on a surface of section for different amplitudes of the oscillating potential. It is found that for small amplitudes, the phase space consists of nonescaping KAM islands and an escaping set. The escaping set is made up of a nonhyperbolic set that gives rise to chaotic scattering and remains of KAM islands. For large amplitudes, the phase space contains a Lebesgue measure zero invariant set that gives rise to chaotic scattering. In this regime, we also discuss the physical origin of the Cantor set responsible for the chaotic scattering and calculate its fractal dimension.

Original languageEnglish
Pages (from-to)667-679
Number of pages13
JournalInternational Journal of Bifurcation and Chaos
Issue number3
Publication statusPublished - Sept 1991


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