Tomaschitz, R. (1992). Relativistic chaos in Robertson-Walker cosmologies: The topological structure of space-time and the microscopic dynamics, in: Chaotic Dynamics: Theory and Practice (Patras, Greece, July 11-20, 1991, T. Bountis, ed.) NATO Science Series B 298, Plenum, New York, 1992, pp. 161-175. (CDS, SAO/NASA ADS)

 

 

 

Title:

 

Relativistic chaos in Robertson-Walker cosmologies: The topological structure of space-time and the microscopic dynamics

Authors:

 

Tomaschitz, Roman

Affiliation:

 

AA(Dipartimento di Matematica Pura ed Applicata dell' Università degli Studi di Padova, Via Belzoni 7, I-35131 Padova, Italy)

Publication:

 

Relativistic chaos in Robertson-Walker cosmologies: The topological structure of space-time and the microscopic dynamics, in: Chaotic Dynamics: Theory and Practice (T. Bountis, ed.) NATO Science Series B 298, Plenum, New York, 1992, pp. 161-175

Publication Date:

 

00/1992

Origin:

 

AUTHOR

Keywords:

 

open Robertson-Walker cosmology, multiply connected hyperbolic 3-space, time evolution of quantum

Abstract Copyright:

 

Springer

Bibliographic Code:

 

1992cdtp.book..161T

 

 

 

Fig. 1. Tiling induced on the boundary S∞ of the Poincaré ball B3 by the universal cover of the 3-manifold I × S. The convex hull of the fractal Jordan curve Λ(Γ) determines a compact region C(Λ)\Γ (see Sec. 3) in the infinite 3-space F, where the chaotic trajectories lie. g(S) = 19, δ = 1.402 ± 0.001 (δ has been calculated by the method of characteristic curves, cf. [15]).

 

Fig. 1. Tiling induced on the boundary S∞ of the Poincaré ball B3 by the universal cover of the 3-manifold I × S. The convex hull of the fractal Jordan curve Λ(Γ) determines a compact region C(Λ)\Γ (see Sec. 3) in the infinite 3-space F, where the chaotic trajectories lie. g(S) = 19, δ = 1.402 ± 0.001 (δ has been calculated by the method of characteristic curves, cf. [15]). full size image

 

 

 

Fig. 2. As Fig. 1, covering of S∞ stemming from a spacelike section F of the 4-manifold. Fig. 1(b) in [14] – Fig. 1 – Fig. 2 – Fig. 2 in [16] represent a sequence of non-isometric points on a path (F(t),Γ(t)) in the deformation space of the topological manifold I × S. g(S) = 19, δ = 1.423.

 

Fig. 2. As Fig. 1, covering of S∞ stemming from a spacelike section F of the 4-manifold. Fig. 1(b) in [14] – Fig. 1 – Fig. 2 – Fig. 2 in [16] represent a sequence of non-isometric points on a path  (F(t),Γ(t)) in the deformation space of the topological manifold I × S. g(S) = 19, δ = 1.423. full size image

 

 

description: Roman Tomaschitz (1992) Relativistic chaos in Robertson–Walker cosmologies: The topological structure of space-time and the microscopic dynamics, in: Chaotic Dynamics: Theory and Practice (T. Bountis, ed.) NATO Science Series B 298, Plenum, New York, pp. 161-175.

 

 

Keywords: open Robertson–Walker universe, multiply connected hyperbolic 3-space, constant negative curvature, Klein–Gordon equation and Laplace–Beltrami operator on open hyperbolic 3-manifolds, cosmic time evolution of scalar quantum fields, Poincaré ball model of hyperbolic geometry, universal covering space, polyhedral tessellation of hyperbolic space, limit sets of Kleinian groups, quasi-Fuchsian covering groups, hyperbolic convex hull of a fractal limit set, Hausdorff dimension, covering projection, mixing in the chaotic nucleus of the open 3-space, Bernoulli property, time evolution of chaotic world lines, deformation spaces of fibered hyperbolic 3-manifolds, compact Riemann surfaces

 

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