Algebraic curves A◦l (x) − U(y) = 0 and arithmetic of orbits of rational functions

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3 Scopus citations


We give a description of pairs of complex rational functions A and U of degree at least two such that for every d1 the algebraic curve A◦d (x) −U(y) = 0 has a factor of genus zero or one. In particular, we show that if A is not a “generalized Lattès map”, then this condition is satisfied if and only if there exists a rational function V such that U ◦ V = A◦l for some l ≥ 1. We also prove a version of the dynamical Mordell–Lang conjecture, concerning intersections of orbits of points from P1 (K) under iterates of A with the value set U(P1 (K)), where A and U are rational functions defined over a number field K.

Original languageEnglish
Pages (from-to)153-183
Number of pages31
JournalMoscow Mathematical Journal
Issue number1
StatePublished - 1 Jan 2020


  • Dynamical Mordell
  • Lang conjecture
  • Riemann surface orbifolds
  • Semiconjugate rational functions
  • Separated variable curves

ASJC Scopus subject areas

  • Mathematics (all)


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