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

TL;DR

This paper extends the generalized ergodic theory to Cantor-systems, exploring the concept of ultrasensitivity and its implications for chaos and regularity within these systems.

Contribution

It introduces a new perspective on sensitivity in Cantor-systems, defining ultrasensitivity and analyzing its role in generalized chaos and system regularity.

Findings

Ultrasensitive sources can generate generalized chaos.

Conditions of generalized continuity influence chaos regularity.

Sensitivity concepts are extended beyond metric frameworks.

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.