Positive Hausdorff dimension for the survivor set and transitions to chaos for piecewise smooth maps

Abstract: We consider two related problems. The transition to chaos in the sense of positive topological entropy for one-dimensional piecewise smooth maps, and the transition to positive Hausdorff dimension for the survivor set of associated open maps. We describe an iterative process that determines the boundaries of positive topological entropy (resp. positive Hausdorff dimension). The boundary can then be characterised via substitution sequences that generalise the Thue-Morse sequence for continuous maps of the interval. This work is joint with Clément Hege.

dynamical systemsnumber theory

Audience: researchers in the topic

( paper | slides )

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One World Numeration seminar

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