Forcing of periodic orbits for interval maps and renormalization of piecewise affine maps

Details Forcing of periodic orbits for interval maps and renormalization of piecewise affine maps Forcing of periodic orbits for interval maps and renormalization of piecewise affine maps

1994-10-17

arxiv.org/abs/math/9410223v1

Mathematics

Dynamical Systems

Scientific paper

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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