Fractal structures of spheroidal chaotic attractors

A three-dimensional generic map exhibiting spheroidal attractors of all types of dynamics possible in three dimensions is introduced. The map is designed to easily invert the stability features of the spheroidal attractors giving rise to repellors or basin boundaries of locally similar geometric properties. For the three different types of ordinary chaos with one positive Lyapunov characteristic exponent a criterion is provided for the close correlation between chaotic dynamics and fractal structures.