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Fractal Dimensions in Dynamics

Name: Fractal Dimensions in Dynamics
Keywords: porosity, box dimension, thermodynamic formalism, Julia set, Hausdorff dimension, Henon attractor, hyperbolic measures, Navier-Stokes equation, limit cycle, horseshoe

descriptionPublicationkeyboard_double_arrow_right Part of book or chapter of book , Other literature type 01 Jan 2006Publisher:Elsevier BV

Authors: Vesna Županović; Darko Žubrinić;

doi: 10.1016/b0-12-512666-2/00373-4

Fractal Dimensions in Dynamics

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Abstract

This is an invited article for the Encyclopedia of Mathematical Physics, published by Elsevier in Oxford in 2006. We describe some basic methods of fractal analysis in dynamics. A special emphasis is on the computation of Hausdorff and box dimensions. In particular, we present dimension results for the logistic map, Smale horseshoe, Lorenz and Henon attractors, Julia and Mandelbrot sets, spiral trajectories, attractors appearing in infinite-dimensional systems, and Brownian motion trajectories.

Related Organizations

University of Zagreb
Croatia

Keywords

porosity, box dimension, thermodynamic formalism, Julia set, Hausdorff dimension, Henon attractor, hyperbolic measures, Navier-Stokes equation, limit cycle, horseshoe, Minkowski content and lacunarity, Lyapunov dimension, Mandelbrot set, Lorenz attractor

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