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 |
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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 journal › Article
}
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 -