منابع مشابه
Constructing Locally Connected Non-computable Julia Sets
A locally connected quadratic Siegel Julia set has a simple explicit topological model. Such a set is computable if there exists an algorithm to draw it on a computer screen with an arbitrary resolution. We constructively produce parameter values for Siegel quadratics for which the Julia sets are non-computable, yet locally connected.
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W. L. Ayres and H. M. Gehman have proved independently that if a locally connected continuum S contains a non-cut point p, there exists an arbitrarily small region R containing p and such that S — R is connected. Our paper is concerned with certain generalizations of this theorem. We shall consider a space 5 which is a locally connected continuum and contains a closed set P such that S — P is c...
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We describe examples of rational maps which are not topologically conjugate to a polynomial and whose Julia sets are connected but not locally connected. Introduction and motivations The dynamics of a rational map f acting on Ĉ is concentrated on its Julia set which is (by definition) the minimal compact set invariant by f and f−1 containing at least three points. The question of local connecti...
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ژورنال
عنوان ژورنال: Proceedings of the National Academy of Sciences
سال: 1938
ISSN: 0027-8424,1091-6490
DOI: 10.1073/pnas.24.9.392