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Partial hyperbolicity and specification

Authors: Naoya Sumi, Paulo Varandas and Kenichiro Yamamoto
Journal: Proc. Amer. Math. Soc. 144 (2016), 1161-1170
MSC (2010): Primary 37D25, 37D30
Published electronically: August 20, 2015
MathSciNet review: 3447669
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Abstract: We study the specification property for partially hyperbolic dynamical systems. In particular, we show that if a partially hyperbolic diffeomorphism has two saddles with different indices, and the stable manifold of one of these saddles coincides with the strongly stable leaf, then it does not satisfy the specification property.

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Naoya Sumi
Affiliation: Department of Mathematics, Faculty of Science, Kumamoto University, 2-39-1 Kurokami, Kumamoto-shi, Kumamoto, 860-8555, Japan

Paulo Varandas
Affiliation: Departamento de Mathemática, Universidade Federal da Bahia, Ademar de barros S/N, 20170-110 Sulvador, Brazil

Kenichiro Yamamoto
Affiliation: Department of General Education, Nagaoka University of Technology, Niigata 940-2188, Japan

Keywords: Specification, partially hyperbolic, robustly non-hyperbolic transitive
Received by editor(s): October 13, 2014
Received by editor(s) in revised form: February 26, 2015
Published electronically: August 20, 2015
Communicated by: Yingfei Yi
Article copyright: © Copyright 2015 American Mathematical Society