### Abstract

We consider particle motion in nonautonomous 1 degree of freedom Hamiltonian systems for which H (p, q, t) depends on N periodic functions of t with incommensurable frequencies. It is shown that in near-integrable systems of this type, phase space is partitioned into nonintersecting regular and chaotic regions. In this respect there is no difference between the N = 1 (periodic time dependence) and the N = 2, 3,... (quasi-periodic time dependence) problems. An important consequence of this phase space structure is that the mechanism that leads to fractal properties of chaotic trajectories in systems with N = 1 also applies to the larger class of problems treated here. Implications of the results presented to studies of ray dynamics in two-dimensional waveguides and particle motion in two-dimensional incompressible fluid flows are discussed.

Original language | English (US) |
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Pages (from-to) | 69-74 |

Number of pages | 6 |

Journal | Nonlinear Processes in Geophysics |

Volume | 5 |

Issue number | 2 |

State | Published - Jun 1 1998 |

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### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Geophysics
- Geochemistry and Petrology