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Transactions of the American Mathematical Society

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

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Computing geometric Lorenz attractors with arbitrary precision
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by D. S. Graça, C. Rojas and N. Zhong PDF
Trans. Amer. Math. Soc. 370 (2018), 2955-2970 Request permission

Abstract:

The Lorenz attractor was introduced in 1963 by E. N. Lorenz as one of the first examples of strange attractors. However, Lorenz’ research was mainly based on (non-rigorous) numerical simulations, and, until recently, the proof of the existence of the Lorenz attractor remained elusive. To address that problem some authors introduced geometric Lorenz models and proved that geometric Lorenz models have a strange attractor. In 2002 it was shown that the original Lorenz model behaves like a geometric Lorenz model and thus has a strange attractor.

In this paper we show that geometric Lorenz attractors are computable, as well as show their physical measures.

References
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Additional Information
  • D. S. Graça
  • Affiliation: Faculdade de Ciências e Tecnologia, Universidade do Algarve, C. Gambelas, 8005-139 Faro, Portugal – and – Instituto de Telecomunicações, Portugal
  • Email: dgraca@ualg.pt
  • C. Rojas
  • Affiliation: Departamento de Matemáticas, Universidad Andres Bello, República 498, 2do piso, Santiago, Chile
  • Email: crojas@mat-unab.cl
  • N. Zhong
  • Affiliation: Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221-0025
  • Email: ning.zhong@uc.edu
  • Received by editor(s): October 5, 2016
  • Received by editor(s) in revised form: December 21, 2016, and February 15, 2017
  • Published electronically: October 31, 2017
  • Additional Notes: The first author was partially supported by Fundação para a Ciência e a Tecnologia and EU FEDER POCTI/POCI via SQIG - Instituto de Telecomunicações through the FCT project UID/EEA/50008/2013.
    The second author was partially supported by projects Fondecyt 1150222, DI- 782-15/R Universidad Andres Bello and Basal PFB-03 CMM-Universidad de Chile.
  • © Copyright 2017 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 370 (2018), 2955-2970
  • MSC (2010): Primary 03D78; Secondary 37D45, 37A35
  • DOI: https://doi.org/10.1090/tran/7228
  • MathSciNet review: 3748590