The resonance overlap criterion and the onset of stochastic behavior in the restricted three-body problem

Details The resonance overlap criterion and the onset of stochastic behavior in the restricted three-body problem The resonance overlap criterion and the onset of stochastic behavior in the restricted three-body problem

Aug 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980aj.....85.1122w&link_type=abstract

Astronomical Journal, vol. 85, Aug. 1980, p. 1122-1133.

Astronomy and Astrophysics

Astronomy

133

Celestial Mechanics, Dynamic Stability, Resonance, Stochastic Processes, Three Body Problem, Entropy, Hamiltonian Functions, Kolmogoroff Theory, Mass Ratios, Nonlinear Equations, Scaling Laws

Scientific paper

The resonance overlap criterion for the onset of stochastic behavior is applied to the planar circular-restricted three-body problem with small mass ratio (mu). Its predictions for mu = 0.001, 0.0001, and 0.00001 are compared to the transitions observed in the numerically determined Kolmogorov-Sinai entropy and found to be in remarkably good agreement. In addition, an approximate scaling law for the onset of stochastic behavior is derived.

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