Erratum: A corrected proof of the scale recurrence lemma from the paper “Stable intersections of regular Cantor sets with large Hausdorff dimensions”

Abstract

This is an erratum for the paper “Stable intersections of regular Cantor sets with large Hausdorff dimensions” by Moreira and Yoccoz. We show how to fix a flaw — a bad choice of parameters — in the proof of the scale recurrence lemma. This lemma is an important step towards establishing the main theorem.

Original article: https://doi.org/10.2307/3062110

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    @MISC{TJE,
      author = {L{ó}pez, J. E.},
      title = {Stable projections of cartesian products of regular {C}antor sets},
      note = {Ph.D. thesis, Instituto Nacional de Matematica Pura e Aplicada},
      year = {2012},
      }
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    @ARTICLE{MY,
      author = {de A. Moreira, C. G. T. and Yoccoz, Jean-Christophe},
      title = {Stable intersections of regular {C}antor sets with large {H}ausdorff dimensions},
      journal = {Ann. of Math. (2)},
      fjournal = {Annals of Mathematics. Second Series},
      volume = {154},
      year = {2001},
      number = {1},
      pages = {45--96},
      issn = {0003-486X},
      mrclass = {37C45 (28A78 28A80 37D05 37E30 37G25)},
      mrnumber = {1847588},
      mrreviewer = {Sergio Plaza},
      doi = {10.2307/3062110},
      url = {https://doi.org/10.2307/3062110},
      zblnumber = {1195.37015},
      }
  • [MY2] Go to document C. G. T. de A. Moreira and J. Yoccoz, "Tangences homoclines stables pour des ensembles hyperboliques de grande dimension fractale," Ann. Sci. Éc. Norm. Supér. (4), vol. 43, iss. 1, pp. 1-68, 2010.
    @ARTICLE{MY2,
      author = {de A. Moreira, C. G. T. and Yoccoz, Jean-Christophe},
      title = {Tangences homoclines stables pour des ensembles hyperboliques de grande dimension fractale},
      journal = {Ann. Sci. \'{E}c. Norm. Supér. (4)},
      fjournal = {Annales Scientifiques de l'\'{E}cole Normale Supérieure. Quatrième Série},
      volume = {43},
      year = {2010},
      number = {1},
      pages = {1--68},
      issn = {0012-9593},
      mrclass = {37D05 (37C45 37E30 37G25)},
      mrnumber = {2583264},
      mrreviewer = {Isabel Lug\~{a}o Rios},
      doi = {10.24033/asens.2115},
      url = {https://doi.org/10.24033/asens.2115},
      zblnumber = {1200.37020},
      }
  • [Z] A. Zamudio, Complex Cantor sets: scale recurrence lemma and dimension formula, 2017.
    @MISC{Z,
      author = {Zamudio, A.},
      title = {Complex {C}antor sets: scale recurrence lemma and dimension formula},
      note = {Ph.D. thesis, Instituto Nacional de Matematica Pura e Aplicada},
      year = {2017},
      }

Authors

Carlos Gustavo T. de A. Moreira

IMPA, Rio de Janeiro, Brazil

Alex Mauricio Zamudio

Universidade Federal Fluminense, Niterói, Brazil