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Open sets of Axiom A flows with exponentially mixing attractors


Authors: V. Araújo, O. Butterley and P. Varandas
Journal: Proc. Amer. Math. Soc. 144 (2016), 2971-2984
MSC (2010): Primary 37D20, 37A25; Secondary 37C10
Published electronically: March 1, 2016
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Abstract: For any dimension $ d\geq 3$ we construct $ \mathcal {C}^{1}$-open subsets of the space of $ \mathcal {C}^{3}$ vector fields such that the flow associated to each vector field is Axiom A and exhibits a non-trivial attractor which mixes exponentially with respect to the unique SRB measure.


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Additional Information

V. Araújo
Affiliation: Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil
Email: vitor.d.araujo@ufba.br, vitor.araujo.im.ufba@gmail.com

O. Butterley
Affiliation: Fakultät für Mathematik, Universität Wien, Oskar-Morgenstern-Platz 1, 1090 Wien, Austria
Address at time of publication: Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, 1-34151 Trieste, Italy
Email: oliver.butterley@univie.ac.at

P. Varandas
Affiliation: Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil
Email: paulo.varandas@ufba.br

DOI: https://doi.org/10.1090/proc/13055
Keywords: Robust exponential decay of correlation, SRB measure, Axiom A flow
Received by editor(s): March 7, 2014
Received by editor(s) in revised form: September 25, 2014, March 19, 2015, and August 28, 2015
Published electronically: March 1, 2016
Additional Notes: The second author is grateful to Henk Bruin for several discussions, and also acknowledges the support of the Austrian Science Fund, Lise Meitner position M1583
The first and third authors were partially supported by CNPq-Brazil, PRONEX-Dyn.Syst. and FAPESB (Brazil).
The authors are deeply grateful to Ian Melbourne for helpful advice and to the anonymous referees for their criticism and many suggestions that helped to improve the article.
Communicated by: Nimish Shah
Article copyright: © Copyright 2016 American Mathematical Society