The formation and evolution of fractal structure within chaotic attractors

Abstract

In this paper we examine in detail the formation and evolution of fractal structure in the chaotic attractors of nonlinear dynamical systems. We explicitly obtain the fractal structure of the underlying chaotic attractors of low-dimensional systems and study their evolution as a system parameter is varied. Using periodic enumeration, dimensional, andf(α) spectral techniques, we obtain a detailed characterization of the multifractal structure.