The construction of a completely scrambled system by graph covers
Takashi Shimomura
TL;DR
This paper introduces a novel method for constructing completely scrambled 0-dimensional dynamical systems using inverse limits of directed graph covers, resulting in transitive systems that lack local equicontinuity.
Contribution
It presents a new construction technique for completely scrambled systems based on graph covers, expanding the class of known examples in topological dynamics.
Findings
Constructed transitive, non-locally equicontinuous systems
Used inverse limits of directed graph covers
Provided new examples of scrambled systems
Abstract
In this paper, we define a new construction of completely scrambled 0-dimensional systems using the inverse limit of sequences of directed graph covers. These examples are transitive and are not locally equicontinuous.
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Taxonomy
TopicsMathematical Dynamics and Fractals · Advanced Topology and Set Theory · Markov Chains and Monte Carlo Methods