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A generalization of Douady's formula

  • * Corresponding author: Gamaliel Blé

    * Corresponding author: Gamaliel Blé 
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  • The Douady's formula was defined for the external argument on the boundary points of the main hyperbolic component $W_0$ of the Mandelbrot set $M$ and it is given by the map $T(θ)=1/2+θ/4$ . We extend this formula to the boundary of all hyperbolic components of $M$ and we give a characterization of the parameter in $M$ with these external arguments.

    Mathematics Subject Classification: Primary: 37F10, 37F45; Secondary: 37F50.


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  • [1] G. Blé, External arguments and invariant measures for the quadratic family, Disc. and Cont. Dyn. Sys., 11 (2004), 241-260.  doi: 10.3934/dcds.2004.11.241.
    [2] A. Douady, Systémes dynamiques holomorphes, Astérisque, (1983), 105-106. 
    [3] A. Douady, Algorithm for computing angles in the Mandelbrot set, Chaotic Dynamics and Fractals, Atlanta 1985, Notes Rep. Math. Sci. Eng., 2 (1986), 155-168. 
    [4] A. Douady and J. H. Hubbard, Étude Dynamique Des Polynômes Complexes I et II, Département de Mathématiques, Orsay, 1985.
    [5] J. Graczyk and S. Smirnov, Non-uniform hyperbolicity in complex dynamics, Invent. Math., 175 (2009), 335-415.  doi: 10.1007/s00222-008-0152-8.
    [6] J. H. Hubbard, Local connectivity of Julia sets and bifurcation loci: Three theorems of J.-C. Yoccoz, Topological Methods in Modern Mathematics, (1993), 467-511. 
    [7] M. Lyubich, Dynamics of quadratic polynomials Ⅰ-Ⅱ, Acta Math, 178 (1997), 185-297.  doi: 10.1007/BF02392694.
    [8] M. Martens and T. Nowicki, Invariant measures for typical quadratic maps, Asterisque, 261 (2000), 239-252. 
    [9] J. Milnor, Dynamics in One Complex Variable, Introductory lectures. Friedr. Vieweg & Sohn, Braunschweig, 1999.
    [10] T. Nowicki and S. van Strien, Invariant measures exist under a summability condition for unimodal maps, Invent. Math., 105 (1991), 123-136.  doi: 10.1007/BF01232258.
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