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arXiv · 1801.05006

Means of iterates

Szyman Draga·Janusz Morawiec
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Abstract

We determine continuous bijections $f$, acting on a real interval into itself, whose $k$-fold iterate is the quasi-arithmetic mean of all its subsequent iterates from $f^0$ up to $f^n$ (where $0\le k\le n$). Namely, we prove that if at most one of the numbers $k,n$ is odd, then such functions consist of at most three affine pieces.

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Szyman Draga, Janusz Morawiec. 2018-01-08. Means of iterates. https://arxiv.org/abs/1801.05006

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