Space guaranteeing a primitive chaotic behavior
Yoshihito Ogasawara, Shin'ichi Oishi

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.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Chaos control and synchronization
