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Bulletin of the American Mathematical Society

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ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Hausdorff Dimension, Lagrange and Markov Dynamical Spectra for Geometric Lorenz Attractors
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by Carlos Gustavo T. Moreira, Maria José Pacifico and Sergio Romaña Ibarra HTML | PDF
Bull. Amer. Math. Soc. 57 (2020), 269-292 Request permission

Abstract:

In this paper, we show that geometric Lorenz attractors have Hausdorff dimension strictly greater than $2$. We use this result to show that for a “large” set of real functions, the Lagrange and Markov dynamical spectrum associated to these attractors has persistently nonempty interior.
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Additional Information
  • Carlos Gustavo T. Moreira
  • Affiliation: Instituto de Matemática Pura e Aplicada (IMPA), Estrada Dona Castorina, 110, 22460-320, Rio de Janeiro, Brazil
  • MR Author ID: 366894
  • Email: gugu@impa.br
  • Maria José Pacifico
  • Affiliation: Instituto de Matemática, Universidade Federal do Rio de Janeiro, C. P. 68.530, CEP 21.945-970, Rio de Janeiro, Brazil
  • MR Author ID: 196844
  • Email: pacifico@im.ufrj.br
  • Sergio Romaña Ibarra
  • Affiliation: Instituto de Matemática, Universidade Federal do Rio de Janeiro, C. P. 68.530, CEP 21.945-970, Rio de Janeiro, Brazil
  • Email: sergiori@im.ufrj.br
  • Received by editor(s): June 16, 2017
  • Published electronically: December 5, 2018
  • Additional Notes: The first author was partially supported by CNPq, PRONEX-Dyn. Syst.
    The second author was partially supported by CNPq, PRONEX-Dyn. Syst., FAPERJ
  • © Copyright 2018 American Mathematical Society
  • Journal: Bull. Amer. Math. Soc. 57 (2020), 269-292
  • DOI: https://doi.org/10.1090/bull/1657
  • MathSciNet review: 4076023