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Volumn 27, Issue 2, 2007, Pages 595-636

A connecting lemma for rational maps satisfying a no-growth condition

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EID: 33947196339     PISSN: 01433857     EISSN: 14694417     Source Type: Journal    
DOI: 10.1017/S0143385706000629     Document Type: Article
Times cited : (44)

References (37)
  • 3
    • 0002221589 scopus 로고
    • Area distortion property of quasi-conformal maps
    • [Ast] K. Astala. Area distortion property of quasi-conformal maps. Acta Math. 173 (1994), 37-60.
    • (1994) Acta Math , vol.173 , pp. 37-60
    • Astala, K.1
  • 4
    • 0042974178 scopus 로고    scopus 로고
    • Infinitesimal perturbations of rational maps
    • [Av] A. Avila. Infinitesimal perturbations of rational maps. Nonlinearity 15 (2002), 695-704.
    • (2002) Nonlinearity , vol.15 , pp. 695-704
    • Avila, A.1
  • 5
    • 33947247331 scopus 로고    scopus 로고
    • Expansion of derivatives in one dimensional dynamics
    • [BS] H. Bruin and S. van Strien. Expansion of derivatives in one dimensional dynamics. Israel J. Math. 137 (2003), 223-263.
    • (2003) Israel J. Math , vol.137 , pp. 223-263
    • Bruin, H.1    van Strien, S.2
  • 6
    • 0002525106 scopus 로고
    • Positive Liapunov exponents and absolute continuity for maps of the interval
    • [CE] P. Collet and J. P. Eckmann. Positive Liapunov exponents and absolute continuity for maps of the interval. Ergod. Th. & Dynam. Sys. 3 (1983), 13-46.
    • (1983) Ergod. Th. & Dynam. Sys , vol.3 , pp. 13-46
    • Collet, P.1    Eckmann, J.P.2
  • 8
    • 0001539882 scopus 로고
    • On the dynamics of polynomial-like mappings
    • DH1
    • [DH1] A. Douady and J. Hubbard. On the dynamics of polynomial-like mappings. Ann. Sci. École Norm. Sup. (2) 18 (1985), 287-344.
    • (1985) Ann. Sci. École Norm. Sup , vol.18 , Issue.2 , pp. 287-344
    • Douady, A.1    Hubbard, J.2
  • 9
    • 33846181504 scopus 로고
    • A proof of Thurston's topological characterization of rational functions
    • DH2
    • [DH2] A. Douady and J. H. Hubbard. A proof of Thurston's topological characterization of rational functions. Acta Math. 171 (1993), 263-297.
    • (1993) Acta Math , vol.171 , pp. 263-297
    • Douady, A.1    Hubbard, J.H.2
  • 10
    • 0001169771 scopus 로고
    • Hausdorff and conformal measures on Julia sets with rationally indifferent periodic points
    • [DU] M. Denker and M. Urbański. Hausdorff and conformal measures on Julia sets with rationally indifferent periodic points. J. London Math. Soc. (2) 43 (1991), 107-118.
    • (1991) J. London Math. Soc. (2) , vol.43 , pp. 107-118
    • Denker, M.1    Urbański, M.2
  • 11
    • 0032378560 scopus 로고    scopus 로고
    • Collet, Eckmann and Holder
    • GSm1
    • [GSm1] J. Graczyk and S. Smirnov. Collet, Eckmann and Holder. Invent. Math. 133 (1998), 69-96.
    • (1998) Invent. Math , vol.133 , pp. 69-96
    • Graczyk, J.1    Smirnov, S.2
  • 13
    • 0034388590 scopus 로고    scopus 로고
    • Harmonic measure and expansion on the boundary of the connectedness locus
    • [GSw] J. Graczyk and G. Świa̧tek. Harmonic measure and expansion on the boundary of the connectedness locus. Invent. Math. 142 (2000), 605-629.
    • (2000) Invent. Math , vol.142 , pp. 605-629
    • Graczyk, J.1    Świa̧tek, G.2
  • 17
    • 0036041076 scopus 로고    scopus 로고
    • On an analytic approach to the Fatou conjecture
    • [L] G. Levin. On an analytic approach to the Fatou conjecture. Fund. Math. 171 (2002), 177-196.
    • (2002) Fund. Math , vol.171 , pp. 177-196
    • Levin, G.1
  • 19
    • 33644624005 scopus 로고    scopus 로고
    • Remarks on the Ruelle operator and the invariant line fields problem. II
    • [Mak] P. Makienko. Remarks on the Ruelle operator and the invariant line fields problem. II. Ergod. Th. & Dynam. Sys. 25 (2005), 1561-1581.
    • (2005) Ergod. Th. & Dynam. Sys , vol.25 , pp. 1561-1581
    • Makienko, P.1
  • 21
    • 0001147837 scopus 로고
    • Distortion results and invariant Cantor sets of unimodal mappings
    • [Mar] M. Martens. Distortion results and invariant Cantor sets of unimodal mappings. Ergod. Th. & Dynam. Sys. 14 (1994), 331-349.
    • (1994) Ergod. Th. & Dynam. Sys , vol.14 , pp. 331-349
    • Martens, M.1
  • 23
    • 84966207053 scopus 로고
    • Julia sets are uniformly perfect
    • [MR] R. Mañé and L. F. da Rocha. Julia sets are uniformly perfect. Proc. Amer. Math. Soc. 116 (1992), 251-257.
    • (1992) Proc. Amer. Math. Soc , vol.116 , pp. 251-257
    • Mañé, R.1    da Rocha, L.F.2
  • 24
    • 0002046772 scopus 로고
    • Absolutely continuous invariant measures under the summability condition
    • [NS] T. Nowicki and S. van Strein. Absolutely continuous invariant measures under the summability condition. Invent. Math. 105 (1991), 123-136.
    • (1991) Invent. Math , vol.105 , pp. 123-136
    • Nowicki, T.1    van Strein, S.2
  • 25
    • 8344247691 scopus 로고    scopus 로고
    • Bounded geometry of quadrilaterals and variation of multipliers for rational maps
    • [Pil] K. Pilgrim. Bounded geometry of quadrilaterals and variation of multipliers for rational maps. Fund. Math. 182 (2004), 137-150.
    • (2004) Fund. Math , vol.182 , pp. 137-150
    • Pilgrim, K.1
  • 27
    • 33947250052 scopus 로고    scopus 로고
    • Statistical properties of Topological Collet-Eckmann maps. www.arxiv.org/math.DS/0603459
    • to appear
    • [PR] F. Przytycki and J. Rivera-Letelier. Statistical properties of Topological Collet-Eckmann maps. www.arxiv.org/math.DS/0603459. Ann. Sci. École Norm. Sup. to appear.
    • Ann. Sci. École Norm. Sup
    • Przytycki, F.1    Rivera-Letelier, J.2
  • 29
    • 33646869539 scopus 로고    scopus 로고
    • Iterations of holomorphic Collet-Eckmann maps: Conformal and Invariant measures. Appendix: On non-renormalizable quadratic polynomials
    • Pr2
    • [Pr2] F. Przytycki. Iterations of holomorphic Collet-Eckmann maps: Conformal and Invariant measures. Appendix: On non-renormalizable quadratic polynomials. Trans. Amer. Math. Soc. 350 (1998), 717-742.
    • (1998) Trans. Amer. Math. Soc , vol.350 , pp. 717-742
    • Przytycki, F.1
  • 30
    • 0037214440 scopus 로고    scopus 로고
    • Equivalence and topological invariance of conditions for non-uniform hyperbolicity in the iteration of rational maps
    • [PRS] 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.
    • (2003) Invent. Math , vol.151 , pp. 29-63
    • Przytycki, F.1    Rivera-Letelier, J.2    Smirnov, S.3
  • 31
    • 20644439768 scopus 로고    scopus 로고
    • Porosity of Julia sets of non-recurrent and parabolic Collet-Eckmann functions
    • [PU] F. Przytycki and M. Urbański. Porosity of Julia sets of non-recurrent and parabolic Collet-Eckmann functions. Ann. Acad. Sci. Fenn. Math. 26 (2001), 125-154.
    • (2001) Ann. Acad. Sci. Fenn. Math , vol.26 , pp. 125-154
    • Przytycki, F.1    Urbański, M.2
  • 32
    • 33947289878 scopus 로고    scopus 로고
    • Rational maps with decay of geometry: Rigidity, Thurston's algorithm and local connectivity
    • Brook
    • [R] J. Rivera-Letelier. Rational maps with decay of geometry: rigidity, Thurston's algorithm and local connectivity. Institute of Mathematical Sciences Preprint at Stony Brook #2000/11.
    • Institute of Mathematical Sciences Preprint at Stony , Issue.2000 11
    • Rivera-Letelier, J.1
  • 34
    • 0002355816 scopus 로고    scopus 로고
    • Dynamique des polynômes fibrés
    • Université Paris-Sud
    • [Se] O. Sester. Dynamique des polynômes fibrés. Thesis, Université Paris-Sud, 1997.
    • (1997) Thesis
    • Sester, O.1
  • 35
    • 0348248569 scopus 로고    scopus 로고
    • An alternative proof of Mañé's theorem on non-expanding Julia sets
    • The Mandelbrot Set, Theme and Variations, Cambridge University Press, Cambridge
    • [SL] M. Shishikura and Tan Lei. An alternative proof of Mañé's theorem on non-expanding Julia sets. The Mandelbrot Set, Theme and Variations (London Mathematical Society Lecture Note Series, 274). Cambridge University Press, Cambridge, 2000, pp. 265-279.
    • (2000) London Mathematical Society Lecture Note Series , vol.274 , pp. 265-279
    • Shishikura, M.1    Lei, T.2
  • 36
    • 0347368285 scopus 로고    scopus 로고
    • Symbolic dynamics and Collet-Eckmann condition
    • [Sm] S. Smirnov. Symbolic dynamics and Collet-Eckmann condition. Int. Math. Res. Not. 7 (2000), 333-351.
    • (2000) Int. Math. Res. Not , vol.7 , pp. 333-351
    • Smirnov, S.1
  • 37
    • 0038344485 scopus 로고    scopus 로고
    • Measures and dimensions in conformal dynamics
    • [U] M. Urbański. Measures and dimensions in conformal dynamics. Bull. Amer. Math. Soc. 40 (2003), 281-321.
    • (2003) Bull. Amer. Math. Soc , vol.40 , pp. 281-321
    • Urbański, M.1


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