Constructing rational maps from subdivision rules

DOI10.1090/S1088-4173-03-00082-1zbMath1077.37037OpenAlexW1931291564MaRDI QIDQ4827391

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

Publication date: 16 November 2004

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

Full work available at URL: https://doi.org/10.1090/s1088-4173-03-00082-1

zbMATH Keywords

rational mapconformalityfinite subdivision rule

Mathematics Subject Classification ID

Dynamics of complex polynomials, rational maps, entire and meromorphic functions; Fatou and Julia sets (37F10) Hyperbolic groups and nonpositively curved groups (20F67) 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)

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A characterization of Sierpiński carpet rational maps ⋮ Subdivision rules and virtual endomorphisms ⋮ Exponential growth of some iterated monodromy groups ⋮ A positive characterization of rational maps ⋮ Invariant Jordan curves of Sierpiński carpet rational maps ⋮ Expansion properties for finite subdivision rules. I. ⋮ Dimension of elliptic harmonic measure of snowspheres ⋮ Constructing subdivision rules from rational maps ⋮ Conformal tilings II: Local isomorphism, hierarchy, and conformal type ⋮ Expansion complexes for finite subdivision rules. I ⋮ Shape convergence for aggregate tiles in conformal tilings ⋮ Quasisymmetric uniformization and heat kernel estimates ⋮ Expansion complexes for finite subdivision rules. II ⋮ Unnamed Item

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