0000000000034482

AUTHOR

L. J. Roy

showing 2 related works from this author

On the Multifractal Character of the Lorenz Attractor

1992

A detailed analysis of the Lorenz attractor in connection with generalized dimensions is presented in this work. Different methods have been employed to estimate these dimensions. Two of them are of standard type. A new method, based on the minimal spanning tree of the point distribution, is extensively tested in this work. It turns out that the Lorenz attractor is very appropriate for being analyzed through this technique, which produces a very clean estimate of the extrema scaling indices α min and α max . The different methods give qualitatively the same result: The Lorenz attractor has a multifractal character

PhysicsRössler attractorMathematics::Dynamical SystemsPhysics and Astronomy (miscellaneous)Multifractal systemPhysics::Data Analysis; Statistics and ProbabilityLorenz systemMinimum spanning treeNonlinear Sciences::Chaotic DynamicsCharacter (mathematics)Hausdorff dimensionAttractorStatistical physicsScalingProgress of Theoretical Physics
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Hausdorff dimension from the minimal spanning tree

1993

A technique to estimate the Hausdorff dimension of strange attractors, based on the minimal spanning tree of the point distribution is extensively tested in this work. This method takes into account in some sense the infimum requirement appearing in the definition of the Hausdorff dimension. It provides accurate estimates even for a low number of data points and it is especially suited to high-dimensional systems.

CombinatoricsDiscrete mathematicsHausdorff distancePacking dimensionHausdorff dimensionMathematicsofComputing_NUMERICALANALYSISMinkowski–Bouligand dimensionDimension functionHausdorff measureUrysohn and completely Hausdorff spacesEffective dimensionMathematicsPhysical Review E
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