Pasting together Julia sets: a worked out example of mating.
Milnor, John (2004)
Experimental Mathematics
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Displaying similar documents to “Quasisymmetric embedding of self similar surfaces and origami with rational maps.”
Pasting together Julia sets: a worked out example of mating.
Periodic solutions of arbitrary length in a simple integer iteration.
Clark, Dean (2006)
Advances in Difference Equations [electronic only]
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Tan Lei and Shishikura’s example of non-mateable degree 3 polynomials without a Levy cycle
Arnaud Chéritat (2012)
Annales de la faculté des sciences de Toulouse Mathématiques
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After giving an introduction to the procedure dubbed and quickly recalling known results about more classical notions of polynomial mating, we show conformally correct pictures of the slow mating of two degree post critically finite polynomials introduced by Shishikura and Tan Lei as an example of a non matable pair of polynomials without a Levy cycle. The pictures show a limit for the Julia sets, which seems to be related to the Julia set of a degree rational map. We give a conjectural...
Staircase baker's map generates flaring-type time series.
Hartmann, G.C., Radons, G., Diebner, H.H., Rössler, O.E. (2000)
Discrete Dynamics in Nature and Society
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Twisted matings and equipotential gluings
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. ...
Steinhaus chessboard theorem
Władysław Kulpa, Lesƚaw Socha, Marian Turzański (2000)
Acta Universitatis Carolinae. Mathematica et Physica
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On The Notions of Mating
Carsten Lunde Petersen, Daniel Meyer (2012)
Annales de la faculté des sciences de Toulouse Mathématiques
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The different notions of matings of pairs of equal degree polynomials are introduced and are related to each other as well as known results on matings. The possible obstructions to matings are identified and related. Moreover the relations between the polynomials and their matings are discussed and proved. Finally holomorphic motion properties of slow-mating are proved.