Tame rational functions: Decompositions of iterates and orbit intersections release_xy4vib5pwve6nf5326v7qiy4gm

by Fedor Pakovich

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2021  

Abstract

Let A be a rational function of degree at least two on the Riemann sphere. We say that A is tame if the algebraic curve A(x)-A(y)=0 has no factors of genus zero or one distinct from the diagonal. In this paper, we show that if tame rational functions A and B have orbits with infinite intersection, then A and B have a common iterate. We also show that for a tame rational function A decompositions of its iterates A^∘ d, d≥ 1, into compositions of rational functions can be obtained from decompositions of a single iterate A^∘ N for N big enough.
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Date   2021-05-10
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arXiv  2001.05818v3
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