Period doubling, entropy, and renormalization

Details Period doubling, entropy, and renormalization Period doubling, entropy, and renormalization

1995-11-07

arxiv.org/abs/math/9511221v1

Mathematics

Dynamical Systems

Scientific paper

We show that in any family of stunted sawtooth maps, the set of maps whose set of periods is the set of all powers of 2 has no interior point, i.e., the combinatorial description of the boundary of chaos coincides with the topological description. We also show that, under mild assumptions, smooth multimodal maps whose set of periods is the set of all powers of 2 are infinitely renormalizable.

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