# A priori bounds for some infinitely renormalizable quadratics: II. Decorations

Annales scientifiques de l'École Normale Supérieure (2008)

- Volume: 41, Issue: 1, page 57-84
- ISSN: 0012-9593

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topKahn, Jeremy, and Lyubich, Mikhail. "A priori bounds for some infinitely renormalizable quadratics: II. Decorations." Annales scientifiques de l'École Normale Supérieure 41.1 (2008): 57-84. <http://eudml.org/doc/272200>.

@article{Kahn2008,

abstract = {A decoration of the Mandelbrot set $M$ is a part of $M$ cut off by two external rays landing at some tip of a satellite copy of $M$ attached to the main cardioid. In this paper we consider infinitely renormalizable quadratic polynomials satisfying the decoration condition, which means that the combinatorics of the renormalization operators involved is selected from a finite family of decorations. For this class of maps we provea priori bounds. They imply local connectivity of the corresponding Julia sets and the Mandelbrot set at the corresponding parameter values.},

author = {Kahn, Jeremy, Lyubich, Mikhail},

journal = {Annales scientifiques de l'École Normale Supérieure},

language = {eng},

number = {1},

pages = {57-84},

publisher = {Société mathématique de France},

title = {A priori bounds for some infinitely renormalizable quadratics: II. Decorations},

url = {http://eudml.org/doc/272200},

volume = {41},

year = {2008},

}

TY - JOUR

AU - Kahn, Jeremy

AU - Lyubich, Mikhail

TI - A priori bounds for some infinitely renormalizable quadratics: II. Decorations

JO - Annales scientifiques de l'École Normale Supérieure

PY - 2008

PB - Société mathématique de France

VL - 41

IS - 1

SP - 57

EP - 84

AB - A decoration of the Mandelbrot set $M$ is a part of $M$ cut off by two external rays landing at some tip of a satellite copy of $M$ attached to the main cardioid. In this paper we consider infinitely renormalizable quadratic polynomials satisfying the decoration condition, which means that the combinatorics of the renormalization operators involved is selected from a finite family of decorations. For this class of maps we provea priori bounds. They imply local connectivity of the corresponding Julia sets and the Mandelbrot set at the corresponding parameter values.

LA - eng

UR - http://eudml.org/doc/272200

ER -

## References

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- [9] M. Lyubich, Dynamics of quadratic polynomials. I, II, Acta Math. 178 (1997), 185–247, 247–297. Zbl0908.58053MR1459261
- [10] C. T. McMullen, Complex dynamics and renormalization, Annals of Mathematics Studies 135, Princeton University Press, 1994. Zbl0822.30002MR1312365
- [11] J. Milnor, Local connectivity of Julia sets: expository lectures, in The Mandelbrot set, theme and variations, London Math. Soc. Lecture Note Ser. 274, Cambridge Univ. Press, 2000, 67–116. Zbl1107.37305MR1765085
- [12] J. Milnor, Periodic orbits, externals rays and the Mandelbrot set: an expository account (Géométrie complexe et systèmes dynamiques, Orsay, 1995), Astérisque261 (2000), 277–333. Zbl0941.30016MR1755445

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