Let be a rational function of degree at least 2 on the Riemann sphere. We say that is tame if the algebraic curve has no factors of genus 0 or 1 distinct from the diagonal. In this paper, we show that if tame rational functions and have some orbits with infinite intersection, then and have a common iterate. We also show that for a tame rational function decompositions of its iterates into compositions of rational functions can be obtained from decompositions of a single iterate for large enough.
Cite this article
Fedor Pakovich, Tame rational functions: Decompositions of iterates and orbit intersections. J. Eur. Math. Soc. 25 (2023), no. 10, pp. 3953–3978DOI 10.4171/JEMS/1277