Indecomposable Continua and the Julia Sets of Polynomials

DOI10.2307/2159146zbMath0773.30005OpenAlexW4235185050MaRDI QIDQ4695576

James T. jun. Rogers, John C. Mayer

Publication date: 29 June 1993

Full work available at URL: https://doi.org/10.2307/2159146

zbMATH Keywords

Julia setFatou setindecomposable continuumcomplex analytic dynamicssimple dense canal

Mathematics Subject Classification ID

Continua and generalizations (54F15) General theory of conformal mappings (30C35) Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable (30D05) Cluster sets, prime ends, boundary behavior (30D40)

Related Items (7)

Any counterexample to Makienko’s conjecture is an indecomposable continuum ⋮ Is the boundary of a Siegel disk a Jordan curve? ⋮ Characterizing indecomposable plane continua from their complements ⋮ Rotational subsets of the circle under \(z^d\) ⋮ Indecomposable continua and the Julia sets of polynomials. II ⋮ The solar Julia sets of basic quadratic Cremer polynomials ⋮ Building blocks for quadratic Julia sets

Cites Work

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• On stable homeomorphisms and imbeddings of the pseudo arc
• Singularities in the boundaries of local Siegel disks
• The boundary of a simply connected domain
• Intrinsic rotations of simply connected regions and their boundaries
• On internal composants of indecomposable plane continua
• Prime ends and indecomposability
• A fixed point theorem for plane continua

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