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An equivalent characterization of the summability condition for rational maps

Abstract / Introduction Related Papers Cited by
  • We give an equivalent characterization of the summability condition in terms of the backward contracting property defined by Juan Rivera-Letelier, for rational maps of degree at least two which are expanding away from critical points.
    Mathematics Subject Classification: Primary: 37F10; Secondary: 37F15.

    Citation:

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  • [1]

    H. Bruin, J. Rivera-Letelier, W. Shen and S. van Strien, Large derivatives, backward contraction and invariant densities for interval maps, Invent. Math., 172 (2008), 509-533.doi: 10.1007/s00222-007-0108-4.

    [2]

    H. Bruin, W. Shen and S. van Strien, Invariant measures exist without a growth condition, Comm. Math. Phys., 241 (2003), 287-306.

    [3]

    P. Collet and J. Eckmann, Positive Liapunov exponents and absolute continuity for maps of the interval, Ergodic Theory Dynam. Systems, 3 (1983), 13-46.doi: 10.1017/S0143385700001802.

    [4]

    J. Graczyk and S. Smirnov, Collet, Eckmann and Hölder, Invent. Math., 133 (1998), 69-96.doi: 10.1007/s002220050239.

    [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]

    O. Kozlovski and S. van Strien, Local connectivity and quasi-conformal rigidity of non-renormalizable polynomials, Proc. Lond. Math. Soc. (3), 99 (2009), 275-296.doi: 10.1112/plms/pdn055.

    [7]

    H. Li and W. Shen, Dimensions of rational maps satisfying the backward contraction property, Fund. Math., 198 (2008), 165-176.doi: 10.4064/fm198-2-6.

    [8]

    H. Li and W. Shen, On non-uniform hyperbolicity assumptions in one-dimensional dynamics, Science China Math., 53 (2010), 1663-1677.doi: 10.1007/s11425-010-3134-4.

    [9]

    H. Li and W. Shen, Topological invariance of a strong summability condition in one-dimensional dynamics, Int. Math. Res. Not., 8 (2013), 1783-1799.doi: 10.1093/imrn/rns105.

    [10]

    T. Nowicki and D. Sands, Non-uniform hyperbolicity and universal bounds for S-unimodal maps, Invent. Math., 132 (1998), 633-680.doi: 10.1007/s002220050236.

    [11]

    F. Przytycki, Hölder implies Collet-Eckmann, Géométrie complexe et systèes dynamiques (Orsay, 1995), Astérisque, 261 (2000), 385-403.

    [12]

    F. Przytycki and J. Rivera-Letelier, Statistical properties of topological Collet-Eckman maps, Ann. Sci. Ecole Sup. Norm., 40 (2007), 135-178.doi: 10.1016/j.ansens.2006.11.002.

    [13]

    F. Przytycki, J. Rivera-Letelier and S. Smirnov, Equivalence and topological invariance of conditions for non-uniform hyperbolicity in the iteration of rational maps, Invent. Math., 151 (2003), 29-63.doi: 10.1007/s00222-002-0243-x.

    [14]

    J. Rivera-Letelier, A connecting lemma for rational maps satisfying a no growth condition, Ergodic Theory Dynam. Systems, 27 (2007), 595-636.doi: 10.1017/S0143385706000629.

    [15]

    J. Rivera-LetelierAsymptotic expansion of smooth interval maps, preprint, arXiv:1204.3071.

    [16]

    J. Rivera-Letelier and W. ShenStatistical properties of one-dimensional maps under weak hyperbolicity assumptions, preprint, arXiv:1004.0230.

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