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Devil’s carpet of topological entropy and complexity of global dynamical behavior. (English) Zbl 1030.37023

Summary: For bimodal maps the concept of an equal topological entropy class (ETEC) is established by the dual star products. All the infinitely many ETEC plateaus and single points are harmonically organized in the kneading parameter plane, they construct a multifractal devil’s carpet, which possesses a perfect subregion similarity and a dual central symmetry. The entropy devil’s carpet reveals the complexity of global dynamical behavior in the whole parameter plane of bimodal systems.

MSC:

37E05 Dynamical systems involving maps of the interval
37B40 Topological entropy
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