We describe a new proof of the exponential contraction of the Feigenbaum renormalization operator in the hybrid class of the Feigenbaum fixed point. The proof uses the non existence of invariant line fields in the Feigenbaum tower (C. McMullen), the topological convergence (D. Sullivan), and a new infinitesimal argument, different from previous methods by C. McMullen and M. Lyubich.

We prove the Feigenbaum-Coullet-Tresser conjecture on the hyperbolicity of the renormalization transformation of bounded type. This gives the first computer-free proof of the original Feigenbaum observation of the universal parameter scaling laws. We use the Hyperbolicity Theorem to prove Milnor’s conjectures on self-similarity and “hairiness” of the Mandelbrot set near the corresponding parame...

Probability concepts for rule-baaed expert systems are developed that are compatible with probability used in data fusion of imprecise information Procedures for treating probabilistic evidence are presented, which include the effects of statistical dependence. Confidence limits are defined as being proportional to root-mean-square errors in estimates, and a method is outlined that allows the c...

The previously developed general concept of the Gaussian approximation allows the description of the driven stochastic Duung oscillator by ordinary diierential equations. These equations are analysed analytically as well as numerically to investigate the modiication of simple bifurcations and of the Feigenbaum cascade by stochastic forces. Furthermore the method allows a qualitative discussion ...

be illustrated by the reaction to Winograd and Flores’s (1986) recent book Understanding Computers and Cognition. In personal comments, the book and its authors have been savaged. (Winograd, in particular, has been described as a turncoat because the book constitutes such a radical departure from his early work.) Published comments are, of course, more temperate (Vellino et al. 1987) but still ...

Any reader of the paper by Laloux et al. [1] would have been left utterly confused after consulting the time series for the price of Japanese Government Bonds (JGB) around May 1995 looking for a log-periodic power law acceleration in the data. The authors of [1] now confess their error and admit that the prediction date given in [1] was incorrect and that the correct prediction was for August 1...