Abstract
The fractal basin boundary of a two-dimensional discrete dynamical system modelling a chaotic forcing applied to bistability is shown to be identical to the graph of an infinite series F(x,t)= of weighted iterates of an ergodic unimodal interval function f. In the special case, when f is the logistic map in "full chaos", i.e. ƒ: x ↦ 4x(1 - x), F is a nowhere differentiable function of x for each t > exp(-λf) (even equal to the Weierstrass function), where λf >0 is denoting the Lyapunov exponent of f. For further chaotic functions f, nowhere-differentiability is shown to be obvious from computer simulations.
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