## Institute for Mathematical Sciences

## Preprint ims94-17

** M. Martens & C. Tresser**
* Forcing of Periodic Orbits for Interval Maps and Renormalization of Piecewise Affine Maps*

Abstract: We prove that for continuous maps on the interval, the existence of an n-cycle, implies the existence of n-1 points
which interwind the original ones and are permuted by the map.
We then use this combinatorial result to show that piecewise
affine maps (with no zero slope) cannot be infinitely
renormalizable.

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