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Tame rational functions: Decompositions of iterates and orbit intersections.
- Source :
- Journal of the European Mathematical Society (EMS Publishing); 2023, Vol. 25 Issue 10, p3953-3978, 26p
- Publication Year :
- 2023
-
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 A<superscript>0d</superscript>, d ≤1, into compositions of rational functions can be obtained from decompositions of a single iterate A<superscript>0N</superscript> for N large enough. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 14359855
- Volume :
- 25
- Issue :
- 10
- Database :
- Complementary Index
- Journal :
- Journal of the European Mathematical Society (EMS Publishing)
- Publication Type :
- Academic Journal
- Accession number :
- 171356966
- Full Text :
- https://doi.org/10.4171/JEMS/1277