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
Publication statusPublished - Jan 1997
Externally publishedYes

Fingerprint

Non-integrability
universe
Singularity
Chimneys
Asymptotic analysis
Poles
Model
chimneys
Formal Analysis
Transcendental
Accumulate
Asymptotic Analysis
Argand diagram
Pole
Evidence
Branching
Logarithmic
Initial conditions
poles

Keywords

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

ASJC Scopus subject areas

  • Computational Mechanics
  • Mechanics of Materials
  • Mathematics(all)
  • Applied Mathematics
  • Mathematical Physics
  • Statistical and Nonlinear Physics

Cite this

Evidence of a Natural Boundary and Nonintegrability of the Mixmaster Universe Model. / Bountis, T. C.; Drossos, L. B.

In: Journal of Nonlinear Science, Vol. 7, No. 1, 01.1997, p. 45-55.

Research output: Contribution to journalArticle

Bountis, T. C. ; Drossos, L. B. / Evidence of a Natural Boundary and Nonintegrability of the Mixmaster Universe Model. In: Journal of Nonlinear Science. 1997 ; Vol. 7, No. 1. pp. 45-55.
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