Evidence of a Natural Boundary and Nonintegrability of the Mixmaster Universe Model

T. C. Bountis, L. B. Drossos

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

The formal asymptotic analysis of Latifi et al. [4] suggests that the Mixmaster Universe model possesses movable transcendental singularities and thus is nonintegrable in the sense that it does not satisfy the Painlevé property (i.e., singularities with nonalgebraic branching). In this paper, we present numerical evidence of the nonintegrability of the Mixmaster model by studying the singularity patterns in the complex t-plane, where t is the "physical" time, as well as in the complex τ-plane, where τ is the associated "logarithmic" time. More specifically, we show that in the τ-plane there appears to exist a "natural boundary" of remarkably intricate structure. This boundary lies at the ends of a sequence of smaller and smaller "chimneys" and consists of the type of singularities studied in [4], on which pole-like singularities accumulate densely. We also show numerically that in the complex t-plane there appear to exist complicated, dense singularity patterns and infinitely-sheeted solutions with sensitive dependence on initial conditions.

Original languageEnglish
Pages (from-to)45-55
Number of pages11
JournalJournal of Nonlinear Science
Volume7
Issue number1
DOIs
Publication statusPublished - Jan 1 1997

Keywords

  • Mixmaster Universe model
  • Nonintegrability
  • Singularity analysis in complex time

ASJC Scopus subject areas

  • Modelling and Simulation
  • Engineering(all)
  • Applied Mathematics

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