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Devil’s staircase of topological entropy and global metric regularity. (English) Zbl 0961.37504

Summary: A new global regularity, a devil’s staircase of topological entropy, is found in the interval dynamics for the first time. It shows that all Feigenbaum bifurcation processes preserve topological entropy, and the complementary set to the steps of the devil’s staircase is a chaotic set of Lebesgue measure 0.86 (lower bound).

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
26A30 Singular functions, Cantor functions, functions with other special properties
39B12 Iteration theory, iterative and composite equations
37B40 Topological entropy
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