Are three-frequency quasiperiodic orbits to be expected in typical nonlinear dynamical systems

Details Are three-frequency quasiperiodic orbits to be expected in typical nonlinear dynamical systems Are three-frequency quasiperiodic orbits to be expected in typical nonlinear dynamical systems

Aug 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983phrvl..51..339g&link_type=abstract

Physical Review Letters (ISSN 0031-9007), vol. 51, Aug. 1, 1983, p. 339-342. Research supported by the U.S. Department of Energy

Computer Science

Numerical Analysis

39

Nonlinear Systems, Numerical Analysis, Orbit Calculation, Periodic Variations, Stochastic Processes, Turbulence, Fourier Series, Liapunov Functions, Strange Attractors

Scientific paper

The successive destabilization of fluid modes of incommensurate frequency has been proposed as a possible mechanism for the onset of turbulence. However, certain aspects considered in connection with such a mechanism were challenged by Ruelle and Takens (1971). It was shown by Newhouse et al. (1978) that, if one has a system with a phase-space 'flow' consisting of three incommensurate frequencies, then there exist arbitrarily small changes of the system which convert the flow from a quasi-periodic, three-frequency flow to one which is chaotic. It is pointed out that theoretical understanding related to the question of whether one should typically expect to observe three-frequency quasi-periodicity in experiments is currently very incomplete. In connection with the present investigation, a series of numerical experiments is conducted with a view toward making some progress in clarifying the situation. It is found that, for the definite system studied, three-frequency quasi-periodicity can occur and is, in fact, fairly common.

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