TL;DR
This paper establishes conditions under which the infinite product of a continuous map on a compact metric space exhibits omega-chaos, and provides examples of such maps demonstrating unusual chaotic behavior.
Contribution
It introduces sufficient conditions for omega-chaos in infinite products of continuous maps and constructs novel examples of omega-chaotic maps.
Findings
Infinite product maps can be omega-chaotic under certain conditions.
The paper provides explicit examples of omega-chaotic maps with unusual properties.
Abstract
For any continuous self-map of a compact metric space, we provide sufficient conditions under which the infinite direct product of the map is -chaotic. We also apply the result to obtain some examples of unusual -chaotic maps.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Quantum chaos and dynamical systems · Chaos control and synchronization