Further results on the information theory of deterministic functions and its application to pattern recognition

The author derived recently Shannon entropy and Renyi entropy for deterministic maps (different from the concepts which are utilized by physicists in the study of deterministic chaos) and his purpose herein is to extend the theory and to outline its prospects in pattern recognition. Entropies of random and of distributed functions are defined, and then entropic variance, divergence, mean square divergence and cross-entropic variance are obtained in quite a meaningful way. The results so obtained are used to derive identification criteria for pattern recognition, and an approach involving the local maximization of a multi-model landscape function is suggested. Basically, we are so dealing with an information theory without explicitly referring to probability.