Konzepte der abstrakten Ergodentheorie. Zweiter Teil: Sensitive Cantor-Systeme

Abstract

In the first part of our generalized ergodic theory we introduced Cantor-systems, when we managed to prove the generalized ergodic theorem 3.3. The first component of a Cantor-system is a group of the flow and its second component is a set of sets covering the phase-space. Now we continue and we first come across the resistence of the term of metric sensitivity against further generalization. Finding a way of generalization of sensitivity, we understand, that generalized chaos can come out of special sources of sensitivity, which we call ultrasensitive. However there are conditions of generalized continuosity implying, that chaos arising from ultrasensitive sources shows some regularity, which is determined by an equivalence-relation.