A New Approach To The Treatment Of Separatrix Chaos And Its Applications
S. M. Soskin, R. Mannella, O. M. Yevtushenko, I. A. Khovanov, P. V. E. McClintock
备注：
83 pages, review - submitted as a chapter for the book dedicated to George Zaslavsky; several figs. are of reduced quality, original files are available on request from authors
发表信息：
Published in: "Hamitonian Chaos Beyond the KAM Theory", Eds.: A.C.J. Luo, V. Afraimovich; Nolinear Physical Science, Higher Education Press, Beijing; Springer, Heidelberg (2010); pp. 51-142
We consider time-periodically perturbed 1D Hamiltonian systems possessing one or more separatrices. If the perturbation is weak, then the separatrix chaos is most developed when the perturbation frequency lies in the logarithmically small or moderate ranges: this corresponds to the involvement of resonance dynamics into the separatrix chaos. We develop a method matching the discrete chaotic dynamics of the separatrix map and the continuous regular dynamics of the resonance Hamiltonian. The method has allowed us to solve the long-standing problem of an accurate description of the maximum of the separatrix chaotic layer width as a function of the perturbation frequency. It has also allowed us to predict and describe new phenomena including, in particular: (i) a drastic facilitation of the onset of global chaos between neighbouring separatrices, and (ii) a huge increase in the size of the low-dimensional stochastic web.
Drastic facilitation of the onset of global chaos in a periodically driven Hamiltonian system due to an extremum in the dependence of eigenfrequency on energy
