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- Title
Tame rational functions: Decompositions of iterates and orbit intersections.
- Authors
Pakovich, Fedor
- Abstract
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) = 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 A0d, d ≤1, into compositions of rational functions can be obtained from decompositions of a single iterate A0N for N large enough.
- Subjects
DECOMPOSITION method; ALGEBRAIC curves; ITERATIVE methods (Mathematics); RIEMANN hypothesis; MATHEMATICAL functions
- Publication
Journal of the European Mathematical Society (EMS Publishing), 2023, Vol 25, Issue 10, p3953
- ISSN
1435-9855
- Publication type
Article
- DOI
10.4171/JEMS/1277