The analytic structure of dynamical systems and self-similar natural boundaries

Y. F. Chang, J. M. Greene, M. Tabor, J. Weiss

Research output: Contribution to journalArticlepeer-review

52 Scopus citations


In this paper we investigate the analytic, complex-time structure of the movable singularities for several dynamical systems. In general, it is found that there exists a direct connection between the occurencce of a certain type of multiple-valuedness of the singularities and the existence of a class of remarkable, "self-similar" natural boundaries for these systems. An asymptotic description of the distribution of singularities in the natural boundary is developed. This provides a description of the fine-scale structure of these natural boundaries that agrees closely with the numerical calculations.

Original languageEnglish (US)
Pages (from-to)183-207
Number of pages25
JournalPhysica D: Nonlinear Phenomena
Issue number1-2
StatePublished - Jul 1983
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Mathematical Physics
  • Condensed Matter Physics
  • Applied Mathematics


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