## Institute for Mathematical Sciences

## Preprint ims95-13

** J. Hu and C. Tresser**
* Period Doubling, Entropy, and Renormalization*

Abstract: 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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