Preperiodic points of polynomials over global fields

DOI10.1515/CRELLE.2007.055zbMath1156.37009arXivmath/0506480MaRDI QIDQ5421680

Robert L. Benedetto

Publication date: 24 October 2007

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0506480

zbMATH Keywords

Julia setspolynomial mapspreperiodic pointsarithmetics of dynamical systems

Mathematics Subject Classification ID

Arithmetic theory of algebraic function fields (11R58) Small divisors, rotation domains and linearization in holomorphic dynamics (37F50) Polynomials in number theory (11C08) Rational and birational maps (14E05) Polynomials (irreducibility, etc.) (11R09) Dynamical systems over non-Archimedean local ground fields (37P20) Arithmetic properties of periodic points (37P35) Dynamical systems over global ground fields (37P15)

Related Items (19)

Scarcity of cycles for rational functions over a number field ⋮ Bounds for preperiodic points for maps with good reduction ⋮ Good reduction of periodic points on projective varieties ⋮ Some results on the Flynn–Poonen–Schaefer conjecture ⋮ A lower bound on the canonical height for polynomials ⋮ Li-Yorke and Devaney chaotic uniform dynamical systems amongst weighted shifts ⋮ New families satisfying the dynamical uniform boundedness principle over function fields ⋮ Unnamed Item ⋮ A Mahler-type estimate of weighted Fekete sums on the Berkovich projective line ⋮ Dynamical modular curves for quadratic polynomial maps ⋮ Polynomial iteration in characteristic \(p\) ⋮ Dynamical uniform boundedness and the \(abc\)-conjecture ⋮ 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 ⋮ Current trends and open problems in arithmetic dynamics ⋮ Benedetto’s trick and existence of rational preperiodic structures for quadratic polynomials ⋮ Noncommutative algebraic dynamics: ergodic theory for profinite groups ⋮ Canonical Heights and Preperiodic Points for Certain Weighted Homogeneous Families of Polynomials ⋮ Expansions of quadratic maps in prime fields

Cites Work

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• Components and Periodic Points in Non-Archimedean Dynamics
• Closure of Periodic Points Over a Non-Archimedean Field
• Non-Archimedean holomorphic maps and the Ahlfors islands theorem
• The least common multiple and lattice points on hyperbolas
• Reduction, dynamics, and Julia sets of rational functions
• Boundedness results for periodic points on algebraic varieties

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