Splitting of separatrices and symbolic dynamics for some degenerate standard-like maps

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Abstract

We consider standard-like maps of class C1 with parabolic fixed points and such that the second derivative has a jump discontinuity at the fixed points. An asymptotic formula for the splitting of the separatrices is obtained. The structure of certain chaotic set in the stochastic layer around the separatrices is described in terms of symbolic dynamics. It turns out, in particular, that swinging and rotating regimes of motion may alternate in time arbitrarily. Analogous results are stated for the so-called separatrix mapping and for the more smooth standard-like maps.

Original languageEnglish
Pages (from-to)243-272
Number of pages30
JournalPhysica D: Nonlinear Phenomena
Volume63
Issue number3-4
DOIs
StatePublished - 15 Mar 1993
Externally publishedYes

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