Exploiting geometric signatures to accurately determine properties of attractors (Q1343542)

Motivated by the standard notion of the fractal or Hausdorff-Besicovitch dimension, as connected with the number of cubes of size \(L\) needed to cover the attractor, in the \(L \to 0\) limit, the authors introduce the related geometric signature concept. For a chosen covering cube size \(L\), the derivative \(d \log N(L) / d\log L\) with \(N(L)\) the number of cubes, has \(-D\) (\(D\) is the Hausdorff dimension) as a leading contribution. The so introduced function of \(L\) is shown to be useful while estimating dimensions, characterizing lacunarity and type of attractor (self- similar, nonself-similar), and determining the length of transients for attractors.