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Random Wandering Around Homoclinic-like Manifolds in Symplectic Map Chain

Shin-itiro Goto·Kazuhiro Nozaki·Hiroyasu Yamada
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Abstract

We present a method to construct a symplecticity preserving renormalization group map of a chain of weakly nonlinear symplectic maps and obtain a general reduced symplectic map describing its long-time behaviour. It is found that the modulational instability in the reduced map triggers random wandering of orbits around some homoclinic-like manifolds, which is understood as the Bernoulli shifts.

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Shin-itiro Goto, Kazuhiro Nozaki, Hiroyasu Yamada. 2001-12-29. Random Wandering Around Homoclinic-like Manifolds in Symplectic Map Chain. https://doi.org/10.1143/ptp.107.637

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