Konzepte der abstrakten Ergodentheorie. Erster Teil: Abstraktion und Analyse des Attraktorbegriffes

TL;DR

This paper develops a generalized ergodic theory focusing on the logical structure of attractors and sensitivity of flows, establishing a broad ergodic theorem applicable to insensitive flows, as a foundation for future work.

Contribution

It introduces a new conceptual framework for attractors and sensitivity in ergodic theory, extending beyond traditional topological approaches.

Findings

Proves a very general ergodic theorem for insensitive flows.

Analyzes the logical structure of attractors.

Prepares groundwork for studying sensitivity of flows in future work.

Abstract

Our conception of a generalized ergodic theory shall exceed the generality of general topology: In this first part of the generalized ergodic theory we investigate the logical constitution of the conception of attractors. We prepare a general theory of sensitivity of flows, which we intend to present in the second part of the generalized ergodic theory. As a result of this first part take the theorem 3.3 and the theorem 3.8: We show a very general ergodic theorem, however it concerns insensitve flows only.