FRACTAL FEATURES OF INVARIANT-SETS IN A 3-DIMENSIONAL MAP

A three dimensional (3D) map with spheroidal dynamics is studied. The map exhibits all known types of attracting dynamics possible in 3D sta te space. Furthermore, the map allows explicit manipulation of stabili ty features. Thus, spheroidal attractors can be turned into spheroidal repellers or basin boundaries of locally similar topological properti es. The link between chaotic dynamics and fractal structures is illust rated with the aid of basin boundaries corresponding to the three diff erent types of chaotic attractors with one positive Lyapunov character istic exponent.