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Bulletin of the American Mathematical Society

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Hausdorff Dimension, Lagrange and Markov Dynamical Spectra for Geometric Lorenz Attractors


Authors: Carlos Gustavo T. Moreira, Maria José Pacifico and Sergio Romaña Ibarra
Journal: Bull. Amer. Math. Soc.
DOI: https://doi.org/10.1090/bull/1657
Published electronically: December 5, 2018
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Abstract | References | Additional Information

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
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
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

DOI: https://doi.org/10.1090/bull/1657
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
Article copyright: © Copyright 2018 American Mathematical Society