The role of complex-time singularities in chaotic dynamics

A. Goriely, Michael Tabor

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

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
Volume3
Issue number3
StatePublished - 1998

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Chaotic Dynamics
Invariant Manifolds
Singularity
Singularity Analysis
Local Solution
Integrable Systems
Vector Field
Sufficient Conditions
Estimate
Demonstrate

ASJC Scopus subject areas

  • Mathematics (miscellaneous)

Cite this

The role of complex-time singularities in chaotic dynamics. / Goriely, A.; Tabor, Michael.

In: Regular and Chaotic Dynamics, Vol. 3, No. 3, 1998, p. 32-44.

Research output: Contribution to journalArticle

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