Induced expansion for quadratic polynomials
Jacek Graczyk; Grzegorz Świątek
Annales scientifiques de l'École Normale Supérieure (1996)
- Volume: 29, Issue: 4, page 399-482
- ISSN: 0012-9593
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topGraczyk, Jacek, and Świątek, Grzegorz. "Induced expansion for quadratic polynomials." Annales scientifiques de l'École Normale Supérieure 29.4 (1996): 399-482. <http://eudml.org/doc/82413>.
@article{Graczyk1996,
author = {Graczyk, Jacek, Świątek, Grzegorz},
journal = {Annales scientifiques de l'École Normale Supérieure},
keywords = {box mapping; decay of box geometry; expansion-inducing map; Schwarzian derivative},
language = {eng},
number = {4},
pages = {399-482},
publisher = {Elsevier},
title = {Induced expansion for quadratic polynomials},
url = {http://eudml.org/doc/82413},
volume = {29},
year = {1996},
}
TY - JOUR
AU - Graczyk, Jacek
AU - Świątek, Grzegorz
TI - Induced expansion for quadratic polynomials
JO - Annales scientifiques de l'École Normale Supérieure
PY - 1996
PB - Elsevier
VL - 29
IS - 4
SP - 399
EP - 482
LA - eng
KW - box mapping; decay of box geometry; expansion-inducing map; Schwarzian derivative
UR - http://eudml.org/doc/82413
ER -
References
top- [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). Zbl0665.58024MR91e:58101
- [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). Zbl0812.30008MR94d:30044
- [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). Zbl0587.30028MR87f:58083
- [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).
- [6] J. GUCKENHEIMER, Limit sets of S-unimodal maps with zero entropy (Commun. Math. Phys., Vol. 110, 1987, pp. 655-659). Zbl0625.58027MR88i:58111
- [7] J. GUCKENHEIMER and S. JOHNSON, Distortion of S-unimodal maps (Annals of Math., Vol. 132, 1990, pp. 71-130). Zbl0708.58007MR91g:58157
- [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). Zbl0721.58018
- [9] M. JAKOBSON, Absolutely continuous invariant measures for one-parameter families of one-dimensional maps (Commun. Math. Phys., Vol. 81, 1981, pp. 39-88). Zbl0497.58017MR83j:58070
- [10] M. JAKOBSON and G. ŚWIATEK, Metric properties of non-renormalizable S-unimodal maps (preprint IHES, no. IHES/M/91/16, 1991). Zbl0830.58019
- [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). Zbl0138.30301MR32 #5872
- [14] M. LYUBICH, Milnor's attractors, persistent recurrence and renormalization, in (Topological methods in modern mathematics, Publish or Perish, Inc., Houston TX, 1993). Zbl0797.58050MR94e:58082
- [15] M. LYUBICH and J. MILNOR, The dynamics of the Fibonacci polynomial (Jour. of the AMS, Vol. 6, 1993, pp. 425-457). Zbl0778.58040MR93h:58080
- [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). Zbl0791.58003MR95a:58035
- [19] C. PRESTON, Iterates of maps on an interval (Lecture Notes in Mathematics, Vol. 999, Berlin, Heidelberg, New York : Springer, 1983). Zbl0582.58001MR85c:58058
- [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). Zbl0936.37016
- [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). Zbl0020.23801JFM64.0313.06
- [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). Zbl0723.58026MR92h:58106
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