Constructing subdivision rules from rational maps

DOI10.1090/S1088-4173-07-00167-1zbMath1138.37023arXivmath/0703475MaRDI QIDQ5448889

James W. Cannon, Walter R. Parry, William J. Floyd

Publication date: 7 March 2008

Published in: Conformal Geometry and Dynamics of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0703475

zbMATH Keywords

conformalityfinite subdivision rule

Mathematics Subject Classification ID

Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Low-dimensional topology of special (e.g., branched) coverings (57M12) Tilings in (2) dimensions (aspects of discrete geometry) (52C20) Combinatorics and topology in relation with holomorphic dynamical systems (37F20)

Related Items (9)

Subdivision rules and virtual endomorphisms ⋮ Invariant Peano curves of expanding Thurston maps ⋮ Invariant graphs of rational maps ⋮ Topological substitution for the aperiodic Rauzy fractal tiling ⋮ Lattès maps and finite subdivision rules ⋮ Invariant Jordan curves of Sierpiński carpet rational maps ⋮ Expansion properties for finite subdivision rules. I. ⋮ Combinatorial models of expanding dynamical systems ⋮ Expansion properties for finite subdivision rules II

Cites Work

• Unnamed Item
• Quasiconformal homeomorphisms and dynamics. I: Solution of the Fatou- Julia problem on wandering domains
• A proof of Thurston's topological characterization of rational functions
• Combinations of complex dynamical systems
• Recognizing constant curvature discrete groups in dimension 3
• Finite subdivision rules
• Constructing rational maps from subdivision rules
• Expansion complexes for finite subdivision rules. I
• Canonical Thurston obstructions

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