Dynamics of quadratic polynomials : complex bounds for real maps

Mikhail Lyubich; Michael Yampolsky

Annales de l'institut Fourier (1997)

  • Volume: 47, Issue: 4, page 1219-1255
  • ISSN: 0373-0956

Abstract

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We prove complex bounds for infinitely renormalizable real quadratic maps with essentially bounded combinatorics. This is the last missing ingredient in the problem of complex bounds for all infinitely renormalizable real quadratics. One of the corollaries is that the Julia set of any real quadratic map z z 2 + c , c [ - 2 , 1 / 4 ] , is locally connected.

How to cite

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Lyubich, Mikhail, and Yampolsky, Michael. "Dynamics of quadratic polynomials : complex bounds for real maps." Annales de l'institut Fourier 47.4 (1997): 1219-1255. <http://eudml.org/doc/75261>.

@article{Lyubich1997,
abstract = {We prove complex bounds for infinitely renormalizable real quadratic maps with essentially bounded combinatorics. This is the last missing ingredient in the problem of complex bounds for all infinitely renormalizable real quadratics. One of the corollaries is that the Julia set of any real quadratic map $z\mapsto z^2+c$, $c\in [-2,1/4]$, is locally connected.},
author = {Lyubich, Mikhail, Yampolsky, Michael},
journal = {Annales de l'institut Fourier},
keywords = {one-dimensional dynamics; renormalization; quadratic polynomials; complex bounds; local connectivity},
language = {eng},
number = {4},
pages = {1219-1255},
publisher = {Association des Annales de l'Institut Fourier},
title = {Dynamics of quadratic polynomials : complex bounds for real maps},
url = {http://eudml.org/doc/75261},
volume = {47},
year = {1997},
}

TY - JOUR
AU - Lyubich, Mikhail
AU - Yampolsky, Michael
TI - Dynamics of quadratic polynomials : complex bounds for real maps
JO - Annales de l'institut Fourier
PY - 1997
PB - Association des Annales de l'Institut Fourier
VL - 47
IS - 4
SP - 1219
EP - 1255
AB - We prove complex bounds for infinitely renormalizable real quadratic maps with essentially bounded combinatorics. This is the last missing ingredient in the problem of complex bounds for all infinitely renormalizable real quadratics. One of the corollaries is that the Julia set of any real quadratic map $z\mapsto z^2+c$, $c\in [-2,1/4]$, is locally connected.
LA - eng
KW - one-dimensional dynamics; renormalization; quadratic polynomials; complex bounds; local connectivity
UR - http://eudml.org/doc/75261
ER -

References

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