Phase space structure and fractal trajectories in 1 1/2 degree of freedom Hamiltonian systems whose time dependence is quasiperiodic

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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 languageEnglish (US)
Pages (from-to)69-74
Number of pages6
JournalNonlinear Processes in Geophysics
Issue number2
StatePublished - Jun 1 1998


ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Geophysics
  • Geochemistry and Petrology

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