Resonant driving of chaotic orbits

Details Resonant driving of chaotic orbits Resonant driving of chaotic orbits

Jun 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995phrve..51.5287k&link_type=abstract

Physical Review E (Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics), Volume 51, Issue 6, June 1995, p

Mathematics

Dynamical Systems

10

Other Topics In Statistical Physics, Thermodynamics, And Nonlinear Dynamical Systems, Kinetic And Transport Theory Of Gases, Stellar Dynamics And Kinematics

Scientific paper

Finite time segments of chaotic orbits in strongly nonintegrable potentials often exhibit complicated power spectra, which, despite being broadband, are dominated by frequencies ω appropriate for ``nearby'' regular orbits. This implies that even low amplitude periodic driving can trigger complicated resonant couplings, evidencing a sensitive dependence on the driving frequency Ω. Numerical experiments involving individual chaotic orbits indicate that the response to a low amplitude time-periodic perturbation, as measured, e.g., by the maximum excursion in energy arising within a given time interval, can exhibit a sensitive dependence on Ω, with substantial structure even on scales δΩ<10-4 times a typical natural frequency ω. Ensembles of chaotic initial conditions driven with a frequency Ω comparable to the natural frequencies of the unperturbed orbits typically display diffusive behavior: The distribution of energy changes, N(δE(t)), at any given time t is Gaussian and the rms value of the change in energy δErms=A(Ω,E)αt1/2, where α denotes the driving amplitude. For fixed energy E, the proportionality constant A is independent of the detailed choice of initial conditions, but can exhibit a complicated dependence on Ω. Potential implications for galactic dynamics are discussed.

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