Specification and partial hyperbolicity for flows

We prove that if a flow exhibits a partially hyperbolic attractor Λ with splitting and two periodic saddles with different indices such that the stable index of one of them coincides with the dimension of E s then it does not satisfy the specification property. In particular, every sectional-hyperbo...

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Bibliographic Details
Published in:Dynamical systems (London, England) England), 2015-10, Vol.30 (4), p.501-524
Main Authors: Sumi, Naoya, Varandas, Paulo, Yamamoto, Kenichiro
Format: Article
Language:English
Subjects:
Dimensional stability
Dynamical systems
geometric Lorenz attractors
partially hyperbolic flows
periodic points
Saddles
specification property
Specifications
Splitting
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Summary:We prove that if a flow exhibits a partially hyperbolic attractor Λ with splitting and two periodic saddles with different indices such that the stable index of one of them coincides with the dimension of E s then it does not satisfy the specification property. In particular, every sectional-hyperbolic attractor with the specification property is hyperbolic. As an application, we prove that no geometric Lorenz attractor satisfies the specification property.
ISSN:1468-9367
1468-9375
DOI:10.1080/14689367.2015.1081380