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Hausdorffization and polynomial twists

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  • We study dynamical equivalence relations on the moduli space $\MP_d$ of complex polynomial dynamical systems. Our main result is that the critical-heights quotient $\MP_d \to \cT_d$* of [4] is the Hausdorffization of a relation based on the twisting deformation of the basin of infinity. We also study relations of topological conjugacy and the Branner-Hubbard wringing deformation.
    Mathematics Subject Classification: Primary: 37F45; Secondary: 54B15.


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  • [1]

    N. Bourbaki, General topology. Chapters 1-4, in "Elements of Mathematics" (Berlin), Springer-Verlag, 1998. (translated from the French, reprint of the 1989 English translation)


    B. Branner and J. H. Hubbard, The iteration of cubic polynomials. I. The global topology of parameter space, Acta Math., 160 (1988), 143-206.doi: 10.1007/BF02392275.


    R. J. Daverman, "Decompositions of Manifolds," AMS Chelsea Publishing, Providence, RI, 2007. (reprint of the 1986 original)


    L. DeMarco and K. Pilgrim, Critical heights on the moduli space of polynomials, Advances in Math., 226 (2011), 350-372.doi: 10.1016/j.aim.2010.06.020.


    L. DeMarco and K. Pilgrim, Polynomial basins of infinity, preprint, 2009.


    A. Douady and J. H. Hubbard, "Étude Dynamique des Polynômes Complexes," volume 84 of Publications Mathématiques d'Orsay, Université de Paris-Sud, Département de Mathématiques, Orsay, 1984.


    Peter Haïssinsky and Tan Lei, Convergence of pinching deformations and matings of geometrically finite polynomials, Fund. Math., 181 (2004), 143-188.doi: 10.4064/fm181-2-4.


    R. Mañé, P. Sad and D. Sullivan, On the dynamics of rational maps, Ann. Sci. Ec. Norm. Sup., 16 (1983), 193-217.


    C. T. McMullen and D. P. Sullivan, Quasiconformal homeomorphisms and dynamics. III. The Teichmüller space of a holomorphic dynamical system, Adv. Math., 135 (1998), 351-395.doi: 10.1006/aima.1998.1726.

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