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Bulletin of the American Mathematical Society

Published by the American Mathematical Society, the Bulletin of the American Mathematical Society (BULL) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.47.

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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