## Institute for Mathematical Sciences

## Preprint ims01-03

** G. Birkhoff, M. Martens and C. Tresser**
* On the scaling structure for period doubling.*

Abstract: We describe the order on the ratios that define the generic universal smooth period doubling Cantor set. We prove that this
set of ratios forms itself a Cantor set, a Conjecture formulated
by Coullet and Tresser in 1977. We also show that the two period
doubling renormalization operators, acting on the codimension one
space of period doubling maps, form an iterated function system
whose limit set contains a Cantor set.

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