Forcing of Periodic Orbits for Interval Maps and Renormalization of Piece Wise Affine Maps
نویسندگان
چکیده
We prove that for continuous maps on the interval, the existence of a 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. Institute of Mathematical Sciences, SUNY at Stony Brook, Stony Brook, NY 11794-3651. I.B.M., Po Box 218, Yorktown Heights, NY 10598. 1 2 MARCO MARTENS AND CHARLES TRESSER
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