ITERATED DIFFERENTIABLE MAPS WITH NOWHERE DIFFERENTIABLE BASIN BOUNDARIES

The fractal basin boundary of a two-dimensional discrete dynamical sys tem modelling a chaotic forcing applied to bistability is shown to bc identical to the graph of an infinite series F(x, t) = SIGMA(k=0)infin ity t(k) f.k(x) of weighted iterates of an ergodic unimodal interval f unction f. In the special case, when f is the logistic map in ''full c haos'', i.e. f: x bar arrow pointing right 4x (1-x), F is a nowhere di fferentiable function of x for each t > exp (-lambda(f)) (even equal t o the Weierstrass function), where lambda(f) > 0 is denoting the Lyapu nov exponent of f. For further chaotic functions f nowhere-differentia bility is shown to be obvious from computer simulations.