Global multifractal relation between topological entropies and fractal dimensions

摘要

In one-dimensional chaotic dynamics, a global multifractal relation between topological entropies and fractal dimensions of arbitrary period-p-tupling attractors is analyzed on all critical (accumulation) points of transitions to chaos, where the Lyapunov characteristic exponent is zero. The global metric regularity of topological entropies versus fractal dimensions is well characterized by the self-similarity. By the fractal interpolation based on the iterated function system, the fractal dimensions of he curves of topological entropies versus capacity dimensions and versus information dimensions are both found to be 1.82. (C) 2004 Elsevier Ltd. All rights reserved.