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Computing geometric Lorenz attractors with arbitrary precision


Authors: D. S. Graça, C. Rojas and N. Zhong
Journal: Trans. Amer. Math. Soc.
MSC (2010): Primary 03D78; Secondary 37D45, 37A35
DOI: https://doi.org/10.1090/tran/7228
Published electronically: October 31, 2017
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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.


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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

DOI: https://doi.org/10.1090/tran/7228
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.
Article copyright: © Copyright 2017 American Mathematical Society