Scrambled Cantor sets
Stefan Geschke, Jan Greb\'ik, and Benjamin D. Miller
TL;DR
This paper demonstrates that Li-Yorke chaos in a dynamical system guarantees the existence of a scrambled Cantor set, linking chaotic behavior to complex fractal structures.
Contribution
It establishes a new connection between Li-Yorke chaos and the existence of scrambled Cantor sets in dynamical systems.
Findings
Li-Yorke chaos implies scrambled Cantor sets
Provides a theoretical link between chaos and fractal structures
Enhances understanding of chaotic dynamics in topology
Abstract
We show that Li-Yorke chaos ensures the existence of a scrambled Cantor set.
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