Finite orbits for rational functions

DOI10.1016/S0019-3577(07)80017-6zbMath1129.14025arXivmath/0512338MaRDI QIDQ2465612

Jung Kyu Canci

Publication date: 7 January 2008

Published in: Indagationes Mathematicae. New Series (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0512338

zbMATH Keywords

rational maps\(S\)-unit equationsfinite orbitsreduction \(\pmod p\)

Mathematics Subject Classification ID

Rational and birational maps (14E05) Arithmetic algebraic geometry (Diophantine geometry) (11G99) Algebraic number theory: global fields (11R99)

Related Items (6)

Scarcity of cycles for rational functions over a number field ⋮ Bounds for preperiodic points for maps with good reduction ⋮ On multiplicative independence of rational function iterates ⋮ On some notions of good reduction for endomorphisms of the projective line ⋮ Preperiodic points for rational functions defined over a global field in terms of good reduction ⋮ Scarcity of finite orbits for rational functions over a number field

Cites Work

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• Cycles for rational maps of good reduction outside a prescribed set
• On equations in S-units and the Thue-Mahler equation
• Finite polynomial orbits in finitely generated domains
• Linear equations in variables which lie in a multiplicative group
• The number of solutions of decomposable form equations
• The equation x+y=1 in finitely generated groups
• Polynomial cycles in algebraic number fields
• Polynomial cycles in certain local domains
• Periodic points, multiplicities, and dynamical units.

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