SELF-SIMILAR SEQUENCES AND UNIVERSAL SCALING OF DYNAMICAL ENTROPIES

Symbol sequences play a prominent role in the context of symbolic dyna mics. Important features of a dynamical system are reflected by relate d statistics of subsequences. A dynamical behavior giving rise to a se lf-similar attractor and universal scaling relations, expressed by cri tical exponents, will lead to self-similar statistics of subsequences. In the present paper we show how self-similar distributions of subseq uences, i.e., temporal self-similarity, can be connected with a scalin g relation for dynamical entropies. Moreover, the effect of slightly p erturbing perfectly self-similar sequences by contaminating them with noise is investigated. The achieved results are of importance for phys ical processes marking the borderline between order and chaos.