### 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 language | English |
---|---|

Pages (from-to) | 45-55 |

Number of pages | 11 |

Journal | Journal of Nonlinear Science |

Volume | 7 |

Issue number | 1 |

Publication status | Published - Jan 1997 |

Externally published | Yes |

### Fingerprint

### 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

*Journal of Nonlinear Science*,

*7*(1), 45-55.

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

Research output: Contribution to journal › Article

*Journal of Nonlinear Science*, vol. 7, no. 1, pp. 45-55.

}

TY - JOUR

T1 - Evidence of a Natural Boundary and Nonintegrability of the Mixmaster Universe Model

AU - Bountis, T. C.

AU - Drossos, L. B.

PY - 1997/1

Y1 - 1997/1

N2 - 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.

AB - 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.

KW - Mixmaster Universe model

KW - Nonintegrability

KW - Singularity analysis in complex time

UR - http://www.scopus.com/inward/record.url?scp=0005528068&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0005528068&partnerID=8YFLogxK

M3 - Article

VL - 7

SP - 45

EP - 55

JO - Journal of Nonlinear Science

JF - Journal of Nonlinear Science

SN - 0938-8974

IS - 1

ER -