Tame rational functions: Decompositions of iterates and orbit intersections

Research output: Contribution to journalArticlepeer-review


Let A be a rational function of degree at least 2 on the Riemann sphere. We say that A is tame if the algebraic curve A(x) - A(y) D 0 has no factors of genus 0 or 1 distinct from the diagonal. In this paper, we show that if tame rational functions A and B have some 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 large enough.

Original languageAmerican English
Pages (from-to)3953-3978
Number of pages26
JournalJournal of the European Mathematical Society
Issue number10
StatePublished - Oct 2023


  • Orbit intersections
  • decompositions of iterates

All Science Journal Classification (ASJC) codes

  • Applied Mathematics
  • General Mathematics


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