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Tame rational functions: Decompositions of iterates and orbit intersections
release_xy4vib5pwve6nf5326v7qiy4gm
by
Fedor Pakovich
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as a article
.
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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2001.05818v3
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