1. Several extensions have been made, e . g . to interacting wave components, Hamiltonian mechanics, higher-order modulational effects, dissipation effects.
  2. where the amplitudes a, a _ 2, etc . are slowly varying, as are the phases \ alpha, \ alpha _ 2, etc . As for the linear wave case, in lowest order ( as far as modulational effects are concerned ) derivatives of amplitudes and phases are neglected, except for derivatives \ omega and \ boldsymbol { k } of the fast phase \ theta:
  3. Other results obtained by his group include : analysis of the transition to strong chaos in the Fermi-Pasta-Ulam problem; the derivation of the chaos border for the Fermi acceleration model; the numerical computation of the Kolmogorov-Sinai entropy in area-preserving maps; the investigations of weak instabilities in many-dimensional Hamiltonian systems ( Arnold diffusion and modulational diffusion ); the demonstration that the homogeneous models of classical Yang-Mills field have positive Kolmogorov-Sinai entropy, and therefore are generally not integrable; the discovery of the power law decay of Poincar?recurrences in Hamiltonian systems with divided phase space; the demonstration that the dynamics of the Halley comet is chaotic, and is described by a simple map.


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