1998
DOI: 10.1103/physrevlett.80.656
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Chaos in the Einstein-Yang-Mills Equations

Abstract: Yang-Mills color fields evolve chaotically in an anisotropically expanding universe. The chaotic behaviour differs from that found in anisotropic Mixmaster universes. The universe isotropizes at late times, approaching the mean expansion rate of a radiation-dominated universe. However, small chaotic oscillations of the shear and color stresses continue indefinitely. An invariant, coordinate-independent characterisation of the chaos is provided by means of fractal basin boundaries. CfPA-97-TH-06Yang-Mills field… Show more

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Cited by 55 publications
(74 citation statements)
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References 24 publications
(28 reference statements)
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“…1, which already shows a highly chaotic dynamics prior to symmetry breaking. Following the method of Box-Counting [10][11][12]16], around the initial condition (5.6) it is then considered a box in phase space (for the dimensionless variables) of size 10 −5 , inside which a large number of random points are taken (a total of 200.000 random points were used in each run). All initial conditions are then numerically evolved by using an eighthorder Runge-Kutta integration method and the fractal dimension is obtained by statistically studying the outcome of each initial condition at each run of the large set of points.…”
Section: The Dynamical System and Chaotic Behaviormentioning
confidence: 99%
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“…1, which already shows a highly chaotic dynamics prior to symmetry breaking. Following the method of Box-Counting [10][11][12]16], around the initial condition (5.6) it is then considered a box in phase space (for the dimensionless variables) of size 10 −5 , inside which a large number of random points are taken (a total of 200.000 random points were used in each run). All initial conditions are then numerically evolved by using an eighthorder Runge-Kutta integration method and the fractal dimension is obtained by statistically studying the outcome of each initial condition at each run of the large set of points.…”
Section: The Dynamical System and Chaotic Behaviormentioning
confidence: 99%
“…The method we apply in this work for quantifying chaos will then be particularly useful in our planned future applications of our model and it extensions to a cosmological context, in which case other methods may be ambiguous, like, for example, the determination of Lyapunov exponents, which does not give a coordinate invariant measure for chaos, as discussed in [11,12]. Also, other methods for studying chaotic systems, like for example by Poincaré sections, are not suitable in the case we are interested here, in which chaos is a transitory phenomenon as we will see.…”
Section: Introductionmentioning
confidence: 99%
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“…We study chaos in our dynamical system of equations by means of the measure of the fractal dimension (or dimension information) [for a review and definitions, see e.g., Ref. [24]], which gives a topological measure of chaos for different space-time settings and it is a quantity invariant under coordinate transformations, providing then an unambiguous signal for chaos in cosmology and general relativity problems in general [25,26]. The method we apply in this work for quantifying chaos is then particularly useful in this cosmological pre-inflationary scenario context we are studying, in which case other methods may be ambiguous, like, for example, the determination of Lyapunov exponents, which does not give a coordinate invariant measure for chaos, as discussed in [25,26].…”
Section: Introductionmentioning
confidence: 99%
“…[24]], which gives a topological measure of chaos for different space-time settings and it is a quantity invariant under coordinate transformations, providing then an unambiguous signal for chaos in cosmology and general relativity problems in general [25,26]. The method we apply in this work for quantifying chaos is then particularly useful in this cosmological pre-inflationary scenario context we are studying, in which case other methods may be ambiguous, like, for example, the determination of Lyapunov exponents, which does not give a coordinate invariant measure for chaos, as discussed in [25,26]. Also, other methods for studying chaotic systems, like for example by Poincaré sections, are not suitable in the case we are interested here, in which case chaos is mostly a transitory phenomenon (it ends by the time the fields reach the potential minima, or when the inflaton enters the inflationary region).…”
Section: Introductionmentioning
confidence: 99%