Attracting cycles in \(p\)-adic dynamics and height bounds for postcritically finite maps

DOI10.1215/00127094-2804674zbMath1323.37058arXiv1201.1605OpenAlexW2075521556MaRDI QIDQ465457

Rafe Jones, Alon Levy, Robert L. Benedetto, Patrick Ingram

Publication date: 31 October 2014

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1201.1605

zbMATH Keywords

postcritically finiteheights\(p\)-adic dynamicsattracting cyclesBerkovich projective lineLattès maps

Mathematics Subject Classification ID

Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Dynamical systems over non-Archimedean local ground fields (37P20) Families and moduli spaces in arithmetic and non-Archimedean dynamical systems (37P45)

Related Items (12)

A new equivariant in nonarchimedean dynamics ⋮ Minimally critical regular endomorphisms of ⋮ Critical orbits of polynomials with a periodic point of specified multiplier ⋮ The critical height is a moduli height ⋮ Homoclinic orbits, multiplier spectrum and rigidity theorems in complex dynamics ⋮ Berkovich dynamics of Newton maps ⋮ Cyclotomic and abelian points in backward orbits of rational functions ⋮ New normal forms for degree-3 polynomials and rational functions ⋮ Lower bounds for non-Archimedean Lyapunov exponents ⋮ Approximation of non-archimedean Lyapunov exponents and applications over global fields ⋮ Current trends and open problems in arithmetic dynamics ⋮ The minimal resultant locus

Cites Work

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• Thurston's pullback map on the augmented Teichmüller space and applications
• The image of an arboreal Galois representation
• Heegner points and derivatives of \(L\)-series
• Families of rational maps and iterative root-finding algorithms
• A proof of Thurston's topological characterization of rational functions
• Rigid analytic geometry and its applications
• An algebraic characterization of expanding Thurston maps
• The space of rational maps on \(\mathbf P^1\)
• Topology and geometry of the Berkovich ramification locus for rational functions. II
• Teichmüller theory and critically finite endomorphisms
• Isotriviality is equivalent to potential good reduction for endomorphisms of over function fields
• Dessins d'enfants and Hubbard trees
• Nearly Euclidean Thurston maps
• A census of quadratic post-critically finite rational functions defined over
• The space of morphisms on projective space
• Integrality and rigidity for postcritically finite polynomials
• A Finiteness Result for Post-critically Finite Polynomials
• An Ahlfors Islands Theorem for non-archimedean meromorphic functions
• The Fatou set for critically finite maps
• Hubbard trees
• On Thurston's pullback map
• Gauss’ class number problem for imaginary quadratic fields
• On the quasiconformal surgery of rational functions
• The Classification of Critically Preperiodic Polynomials as Dynamical Systems
• Geometry and Dynamics of Quadratic Rational Maps
• Théorie ergodique des fractions rationnelles sur un corps ultramétrique

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