engleski

Fractal dimensions in dynamics

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.

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

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