no. 4
Induced expansion for quadratic polynomials
Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 29 (1996) no. 4, pp. 399-482 
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     author = {Graczyk, Jacek and \'Swi\k{a}tek, Grzegorz},
     title = {Induced expansion for quadratic polynomials},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     pages = {399--482},
     year = {1996},
     publisher = {Elsevier},
     volume = {Ser. 4, 29},
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     url = {https://www.numdam.org/articles/10.24033/asens.1744/}
}
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Graczyk, Jacek; Świątek, Grzegorz. Induced expansion for quadratic polynomials. Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 29 (1996) no. 4, pp. 399-482. doi: 10.24033/asens.1744

[1] A. Blokh and M. Lyubich, Non-existence of wandering intervals and structure of topological attractors for one dimensional dynamical systems (Erg. Th. and Dyn. Sys., Vol. 9, 1989, pp. 751-758). | Zbl | MR

[2] B. Branner and J. H. Hubbard, The iteration of cubic polynomials, Part II : patterns and parapatterns (Acta Math., Vol. 169, 1992, pp. 229-325). | Zbl | MR

[3] A. Douady and J. H. Hubbard, On the dynamics of polynomial-like mappings (Ann. Sci. Ec. Norm. Sup. (Paris), Vol. 18, 1985, pp. 287-343). | Numdam | Zbl | MR | EuDML

[4] J. Graczyk, Ph. D. Thesis (Mathematics Department of Warsaw University (1990) ; also : Dynamics of non-degenerate upper maps, preprint of Queen's University at Kingston, Canada, 1991).

[5] J. Graczyk and G. Światek, Critical circle maps near bifurcation (Stony Brook IMS preprint, 1991, Proposition 2). | Zbl

[6] J. Guckenheimer, Limit sets of S-unimodal maps with zero entropy (Commun. Math. Phys., Vol. 110, 1987, pp. 655-659). | Zbl | MR

[7] J. Guckenheimer and S. Johnson, Distortion of S-unimodal maps (Annals of Math., Vol. 132, 1990, pp. 71-130). | Zbl | MR

[8] F. Hofbauer, F. and G. Keller, Some remarks about recent results on S-unimodal maps (Annales de l'Institut Henri Poincaré, Physique Théorique, Vol. 53, 1990, pp. 413-425). | Numdam | Zbl | EuDML

[9] M. Jakobson, Absolutely continuous invariant measures for one-parameter families of one-dimensional maps (Commun. Math. Phys., Vol. 81, 1981, pp. 39-88). | Zbl | MR

[10] M. Jakobson and G. Światek, Metric properties of non-renormalizable S-unimodal maps (preprint IHES, no. IHES/M/91/16, 1991).

[11] M. Jakobson and G. Światek, Quasisymmetric conjugacies between unimodal maps (Stony Brook preprint, Vol. 16, 1991).

[12] G. Keller and T. Nowicki, Fibonacci maps revisited (manuscript, 1992).

[13] O. Lehto and K. Virtanen, Quasikonforme Abbildungen (Springer-Verlag, Berlin-Heidelberg-New York, 1965). | Zbl | MR

[14] M. Lyubich, Milnor's attractors, persistent recurrence and renormalization, in (Topological methods in modern mathematics, Publish or Perish, Inc., Houston TX, 1993). | Zbl | MR

[15] M. Lyubich and J. Milnor, The dynamics of the Fibonacci polynomial (Jour. of the AMS, Vol. 6, 1993, pp. 425-457). | Zbl | MR

[16] M. Martens, Ph. D. thesis (Math. Department of Delf University of Technology, 1990 ; also : IMS preprint, Vol. 17, 1992).

[17] J. Milnor, The Yoccoz theorem on local connectivity of Julia sets. A proof with pictures (class notes, Stony Brook, 1991-1992).

[18] W. De Melo and S. Van Strien, One-Dimensional Dynamics (Springer-Verlag, New York, 1993). | Zbl | MR

[19] C. Preston, Iterates of maps on an interval (Lecture Notes in Mathematics, Vol. 999, Berlin, Heidelberg, New York : Springer, 1983). | Zbl | MR

[20] D. Sullivan, Bounds, quadratic differentials and renormalization conjectures (to appear in American Mathematical Society Centennial Publications, Vol. 2, American Mathematical Society, Providence, R.I., 1991). | Zbl

[21] G. Światek, Hyperbolicity is dense in the real quadratic family (preprint Stony Brook, 1992).

[22] O. Teichmüller, Untersuchungen über konforme und quasikonforme Abbildung (Deutsche Mathematik, Vol. 3, pp. 621-678). | Zbl | JFM

[23] J.-C. Yoccoz, unpublished results.

[24] J. J. P. Veerman and F. M. Tangerman, Scalings in circle maps (1) (Commun. in Math. Phys., Vol. 134, 1990, pp. 89-107). | Zbl | MR

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