Distributional chaos and factors
Jana Dole\v{z}elov\'a-Hant\'akov\'a
TL;DR
This paper demonstrates that a dynamical system can lack distributionally scrambled pairs while still being semiconjugated to a distributionally chaotic system, revealing nuanced relationships in chaos theory.
Contribution
It introduces the existence of such systems, showing a new complexity in the relationship between distributional chaos and semiconjugation.
Findings
Existence of systems without distributionally scrambled pairs
Semiconjugation to a distributionally chaotic factor is possible without chaos in the original system
Highlights nuanced relationships in distributional chaos theory
Abstract
We show the existence of a dynamical system without any distributionally scrambled pair which is semiconjugated to a distributionally chaotic factor.
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