Preperiodic portraits for unicritical polynomials

DOI10.1090/proc/13075zbMath1368.37051arXiv1501.06821OpenAlexW1551877706MaRDI QIDQ2802109

John R. Doyle

Publication date: 25 April 2016

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.06821

zbMATH Keywords

preperiodic pointunicritical polynomialgeneralized dynatomic polynomial

Mathematics Subject Classification ID

Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Algebraic numbers; rings of algebraic integers (11R04) Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps (37P05)

Related Items (5)

Squarefree doubly primitive divisors in dynamical sequences ⋮ Portraits of preperiodic points for rational maps ⋮ Preperiodic portraits for unicritical polynomials over a rational function field ⋮ Good reduction and Shafarevich-type theorems for dynamical systems with portrait level structures ⋮ Dynamical modular curves for quadratic polynomial maps

Cites Work

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• The dynatomic periodic curves for polynomial \(z\mapsto z^d+c\) are smooth and irreducible
• On some exceptional rational maps
• Symmetries of fractals revisited
• Preperiodic dynatomic curves for $z\mapsto z^d+c$
• Cycles of polynomials in algebraically closed fields of positive characteristic
• Bifurcations and discriminants for polynomial maps
• Cycles of polynomials in algebraically closed fields of positive characteristic (II)
• Portraits of preperiodic points for rational maps
• Determination of all rational preperiodic points for morphisms of PN
• Fixpoints of Polynomials and Rational Functions

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