Quadratic Julia sets with positive area

Pages 673-746 from Volume 176 (2012), Issue 2 by Xavier Buff, Arnaud Chéritat

Abstract

We prove the existence of quadratic polynomials having a Julia set with positive Lebesgue measure. We find such examples with a Cremer fixed point, with a Siegel disk, or with infinitely many satellite renormalizations.

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      VOLUME = {53},
      PAGES = {377--393},
      PUBLISHER = {Amer. Math. Soc.},
      ADDRESS = {Providence, RI},
      YEAR = {2008},
      MRCLASS = {37F25 (37F50)},
      MRNUMBER = {2477430},
      MRREVIEWER = {Peter Ha{ï}ssinsky},
      ZBLNUMBER = {1157.37321},
      }
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    @book{y,
      author={Yoccoz, J. C.},
      TITLE={Petits diviseurs en dimension 1},
      SERIES={Astérisque},
      VOLUME={231},
      PUBLISHER={Soc. Math. France},
      ADDRESS={Paris},
      MRNUMBER = {1367354},
      ZBLNUMBER = {0836.30001},
      YEAR={1995},
     }

Keywords
, , , ,
DOI
http://doi.org/10.4007/annals.2012.176.2.1
MR
2950763
zbMATH
06093940
Milestones
Received: 11 March 2008
Revised: 22 April 2011
Accepted: 13 May 2010
Published online: 1 September 2012

Authors

Xavier Buff

Université de Toulouse
Institut de Mathématiques de Toulouse
118, route de Narbonne
31062 Toulouse
France

Arnaud Chéritat

Université de Toulouse
Institut de Mathématiques de Toulouse
118, route de Narbonne
31062 Toulouse
France