Open sets of Axiom A flows with exponentially mixing attractors
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- by V. Araújo, O. Butterley and P. Varandas
- Proc. Amer. Math. Soc. 144 (2016), 2971-2984
- DOI: https://doi.org/10.1090/proc/13055
- 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.References
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Bibliographic Information
- V. Araújo
- Affiliation: Departamento de Matemática, Universidade Federal da Bahia, Av. Ademar de Barros s/n, 40170-110 Salvador, Brazil
- MR Author ID: 665394
- 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
- MR Author ID: 805760
- 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
- MR Author ID: 857790
- Email: paulo.varandas@ufba.br
- 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
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 144 (2016), 2971-2984
- MSC (2010): Primary 37D20, 37A25; Secondary 37C10
- DOI: https://doi.org/10.1090/proc/13055
- MathSciNet review: 3487229