Space guaranteeing a primitive chaotic behavior

TL;DR

This paper explores conditions under which a Cantor set emerges from generalized chaotic maps, demonstrating that such sets can guarantee infinitely many chaotic behaviors and form a typical continuum.

Contribution

It introduces generalized conditions for chaotic maps that lead to Cantor sets, revealing their role in guaranteeing diverse chaotic behaviors and continuum structures.

Findings

Cantor sets emerge from generalized chaotic maps

Such sets guarantee infinitely many chaotic behaviors

They form a typical continuum

Abstract

This study describes such a situation that a Cantor set emerges as a result of the exploration of sufficient conditions for the property which is generalized from fundamental chaotic maps, and the Cantor set even guarantees infinitely many varieties of the behavior with the property, as well as a typical continuum.