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

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

Research output: Contribution to journalArticle

51 Citations (Scopus)

Abstract

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
Volume8
Issue number1-2
DOIs
StatePublished - 1983
Externally publishedYes

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dynamical systems
Dynamical systems
Dynamical system
Singularity
Numerical Calculation
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ASJC Scopus subject areas

  • Applied Mathematics
  • Statistical and Nonlinear Physics

Cite this

The analytic structure of dynamical systems and self-similar natural boundaries. / Chang, Y. F.; Greene, J. M.; Tabor, Michael; Weiss, J.

In: Physica D: Nonlinear Phenomena, Vol. 8, No. 1-2, 1983, p. 183-207.

Research output: Contribution to journalArticle

Chang, Y. F. ; Greene, J. M. ; Tabor, Michael ; Weiss, J. / The analytic structure of dynamical systems and self-similar natural boundaries. In: Physica D: Nonlinear Phenomena. 1983 ; Vol. 8, No. 1-2. pp. 183-207.
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