Introduction
Pascale Roesch (2012)
Annales de la faculté des sciences de Toulouse Mathématiques
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Pascale Roesch (2012)
Annales de la faculté des sciences de Toulouse Mathématiques
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Paul Blanchard, Daniel Cuzzocreo, Robert L. Devaney, Elizabeth Fitzgibbon, Stefano Silvestri (2014)
Fundamenta Mathematicae
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For the family of rational maps zⁿ + λ/zⁿ where n ≥ 3, it is known that there are infinitely many small copies of the Mandelbrot set that are buried in the parameter plane, i.e., they do not extend to the outer boundary of this set. For parameters lying in the main cardioids of these Mandelbrot sets, the corresponding Julia sets are always Sierpiński curves, and so they are all homeomorphic to one another. However, it is known that only those cardioids that are symmetrically located...
Milnor, John (2000)
Experimental Mathematics
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Xavier Buff, Adam L. Epstein, Sarah Koch, Daniel Meyer, Kevin Pilgrim, Mary Rees, Tan Lei (2012)
Annales de la faculté des sciences de Toulouse Mathématiques
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We survey known results about polynomial mating, and pose some open problems.
Xavier Buff, Thomas Gauthier (2013)
Bulletin de la Société Mathématique de France
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We prove that any Lattès map can be approximated by strictly postcritically finite rational maps which are not Lattès maps.
Bielefeld, Ben, Sutherland, Scott, Tangerman, Folkert, Veerman, J.J.P. (1993)
Experimental Mathematics
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Magnus Aspenberg (2009)
Fundamenta Mathematicae
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We show that Misiurewicz maps for which the Julia set is not the whole sphere are Lebesgue density points of hyperbolic maps.
Stankewitz, Rich, Sugawa, Toshiyuki, Sumi, Hiroki (2004)
Annales Academiae Scientiarum Fennicae. Mathematica
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Xavier Buff, Adam L. Epstein, Sarah Koch (2012)
Annales de la faculté des sciences de Toulouse Mathématiques
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One crucial tool for studying postcritically finite rational maps is Thurston’s topological characterization of rational maps. This theorem is proved by iterating a holomorphic endomorphism on a certain Teichmüller space. The graph of this endomorphism covers a correspondence on the level of moduli space. In favorable cases, this correspondence is the graph of a map, which can be used to study matings. We illustrate this by way of example: we study the mating of the basilica with itself. ...
F. Balibrea, C. La Paz (1997)
Annales Polonici Mathematici
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One-dimensional turbulent maps can be characterized via their ω-limit sets [1]. We give a direct proof of this characterization and get stronger results, which allows us to obtain some other results on ω-limit sets, which previously were difficult to prove.
Lei Tan (2002)
Annales scientifiques de l'École Normale Supérieure
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Mónica Moreno Rocha (2013)
Fundamenta Mathematicae
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An escape time Sierpiński map is a rational map drawn from the McMullen family z ↦ zⁿ + λ/zⁿ with escaping critical orbits and Julia set homeomorphic to the Sierpiński curve continuum. We address the problem of characterizing postcritically finite escape time Sierpiński maps in a combinatorial way. To accomplish this, we define a combinatorial model given by a planar tree whose vertices come with a pair of combinatorial data that encodes the dynamics of critical orbits....