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Renormalization for the boundary of chaos in piecewise monotonic maps with a single discontinuity. (English) Zbl 1418.37069

Summary: Monotonic maps with a single discontinuity arise in a variety of situations. We describe the infinite sets of periods for such maps on the boundary of chaos; this gives a sense of the routes to chaos in such maps. The description involves an explicit subshift of finite type which describes the sequences of different renormalizations possible in these maps.

MSC:

37E05 Dynamical systems involving maps of the interval
37B50 Multi-dimensional shifts of finite type, tiling dynamics (MSC2010)
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37E20 Universality and renormalization of dynamical systems
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