Reduction of dynatomic curves

DOI10.1017/etds.2017.140zbMath1468.37068arXiv1703.04172OpenAlexW2597603672MaRDI QIDQ5235021

John R. Doyle, Simon Rubinstein-Salzedo, Andrew Obus, Lloyd West, Holly Krieger, Rachel J. Pries

Publication date: 7 October 2019

Published in: Ergodic Theory and Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.04172

zbMATH Keywords

combinatoricsMandelbrot setpolynomial mapsramification theorydynatomic modular curvesreduction theory for curves

Mathematics Subject Classification ID

Curves over finite and local fields (11G20) Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Ramification and extension theory (11S15) Ramification problems in algebraic geometry (14E22) Algebraic functions and function fields in algebraic geometry (14H05) Arithmetic and non-Archimedean dynamical systems involving polynomial and rational maps (37P05) Combinatorics and topology in relation with holomorphic dynamical systems (37F20)

Related Items (4)

Moduli spaces for dynamical systems with portraits ⋮ Survey lecture on arithmetic dynamics ⋮ Gonality of dynatomic curves and strong uniform boundedness of preperiodic points ⋮ Current trends and open problems in arithmetic dynamics

Cites Work

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• The dynatomic periodic curves for polynomial \(z\mapsto z^d+c\) are smooth and irreducible
• Squares in arithmetic progression over number fields
• The dynamics of complex polynomials and automorphisms of the shift
• Preperiodic points for rational functions defined over a rational function field of characteristic zero
• Galois groups of periodic points
• Coverings of the affine line in characteristic \(p>0\) and Abhyankar's conjecture
• Cycles of quadratic polynomials and rational points on a genus-2 curve
• Gonality of modular curves in characteristic \(p\)
• Hurwitz schemes and irreducibility of moduli of algebraic curves
• Rational 6-Cycles Under Iteration of Quadratic Polynomials
• Admissibility of kneading sequences and structure of Hubbard trees for quadratic polynomials
• Arithmetic properties of periodic points of quadratic maps, II
• Bifurcations and discriminants for polynomial maps
• Galois Groups and Fundamental Groups
• Gonality of dynatomic curves and strong uniform boundedness of preperiodic points

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