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Ensembles de Julia quadratiques de mesure de Lebesgue strictement positive

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Title: Ensembles de Julia quadratiques de mesure de Lebesgue strictement positive
Alternate Title: Quadratic Julia sets with positive Lebesgue measure
Authors: Buff, Xavier1 xavier.buff@math.ups-tlse.fr, Chéritat, Arnaud1 arnaud.cheritat@math.ups-tlse.fr
Source: Comptes Rendus. Mathématique. Dec2005, Vol. 341 Issue 11, p669-674. 6p.
Subjects: Logical prediction, Quadratic equations, Polynomials, Algebra, Mathematics education
Abstract (English): Abstract: In this Note, we prove a variant of a conjecture stated in the thesis of Chéritat. The proof is based on results announced by Inou and Shishikura, and on earlier results of McMullen and of Chéritat. According to Chéritat''s thesis, this allows us to complete a plan initiated by Douady and to show that there exist quadratic polynomials having a Julia set of positive Lebesgue measure. To cite this article: X. Buff, A. Chéritat, C. R. Acad. Sci. Paris, Ser. I 341 (2005). [Copyright &y& Elsevier]
Abstract (French): Résumé: Dans cette Note, nous prouvons une variante d''''une conjecture énoncée dans la thèse de Chéritat. La preuve est basée sur des résultats annoncés par Inou et Shishikura, ainsi que sur des travaux plus anciens de McMullen et de Chéritat. D''''après la thèse de Chéritat, cela permet de compléter un plan initié par Douady et de prouver l''''existence de polynômes quadratiques dont l''''ensemble de Julia est de mesure strictement positive. Pour citer cet article : X. Buff, A. Chéritat, C. R. Acad. Sci. Paris, Ser. I 341 (2005).
Copyright of Comptes Rendus. Mathématique is the property of Academie des Science, Centre Mersenne and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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  Data: Ensembles de Julia quadratiques de mesure de Lebesgue strictement positive
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  Data: Quadratic Julia sets with positive Lebesgue measure
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  Data: <searchLink fieldCode="AR" term="%22Buff%2C+Xavier%22">Buff, Xavier</searchLink><relatesTo>1</relatesTo><i> xavier.buff@math.ups-tlse.fr</i><br /><searchLink fieldCode="AR" term="%22Chéritat%2C+Arnaud%22">Chéritat, Arnaud</searchLink><relatesTo>1</relatesTo><i> arnaud.cheritat@math.ups-tlse.fr</i>
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  Data: <searchLink fieldCode="DE" term="%22Logical+prediction%22">Logical prediction</searchLink><br /><searchLink fieldCode="DE" term="%22Quadratic+equations%22">Quadratic equations</searchLink><br /><searchLink fieldCode="DE" term="%22Polynomials%22">Polynomials</searchLink><br /><searchLink fieldCode="DE" term="%22Algebra%22">Algebra</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematics+education%22">Mathematics education</searchLink>
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  Data: Abstract: In this Note, we prove a variant of a conjecture stated in the thesis of Chéritat. The proof is based on results announced by Inou and Shishikura, and on earlier results of McMullen and of Chéritat. According to Chéritat''s thesis, this allows us to complete a plan initiated by Douady and to show that there exist quadratic polynomials having a Julia set of positive Lebesgue measure. To cite this article: X. Buff, A. Chéritat, C. R. Acad. Sci. Paris, Ser. I 341 (2005). [Copyright &y& Elsevier]
– Name: Abstract
  Label: Abstract (French)
  Group: Ab
  Data: Résumé: Dans cette Note, nous prouvons une variante d''''une conjecture énoncée dans la thèse de Chéritat. La preuve est basée sur des résultats annoncés par Inou et Shishikura, ainsi que sur des travaux plus anciens de McMullen et de Chéritat. D''''après la thèse de Chéritat, cela permet de compléter un plan initié par Douady et de prouver l''''existence de polynômes quadratiques dont l''''ensemble de Julia est de mesure strictement positive. Pour citer cet article : X. Buff, A. Chéritat, C. R. Acad. Sci. Paris, Ser. I 341 (2005). </ce:abst [Copyright 2005 Elsevier]
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  Data: <i>Copyright of Comptes Rendus. Mathématique is the property of Academie des Science, Centre Mersenne and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – SubjectFull: Polynomials
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