The role of complex-time singularities in chaotic dynamics

A. Goriely, Michael Tabor

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2 Scopus citations


The analysis of complex-time singularities has proved to be the most useful tool for the analysis of integrable systems. Here, we demonstrate its use in the analysis of chaotic dynamics. First, we show that the Melnikov vector, which gives an estimate of the splitting distance between invariant manifolds, can be given explicitly in terms of local solutions around the complex time singularities. Second, in the case of exponentially small splitting of invariant manifolds, we obtain sufficient conditions on the vector field for the Melnikov theory to be applicable. These conditions can be obtained algorithmically from the singularity analysis.

Original languageEnglish (US)
Pages (from-to)32-44
Number of pages13
JournalRegular and Chaotic Dynamics
Issue number3
Publication statusPublished - 1998


ASJC Scopus subject areas

  • Mathematics (miscellaneous)

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