Separatrix chaos: new approach to the theoretical treatment

Details Separatrix chaos: new approach to the theoretical treatment Separatrix chaos: new approach to the theoretical treatment

2007-11-29

arxiv.org/abs/0711.4827v1

Nonlinear Sciences

Chaotic Dynamics

10 pages, 4 figures, proceedings of the conference "Chaos, Complexity and Transport" (Marseille, 5-9 June 2007), in press

Scientific paper

We develop a new approach to the theoretical treatment of the separatrix chaos, using a special analysis of the separatrix map. The approach allows us to describe boundaries of the separatrix chaotic layer in the Poincar\'{e} section and transport within the layer. We show that the maximum which the width of the layer in energy takes as the perturbation frequency varies is much larger than the perturbation amplitude, in contrast to predictions by earlier theories suggesting that the maximum width is of the order of the amplitude. The approach has also allowed us to develop the self-consistent theory of the earlier discovered (PRL 90, 174101 (2003)) drastic facilitation of the onset of global chaos between adjacent separatrices. Simulations agree with the theory.

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