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ISSN 1088-6826(e) ISSN 0002-9939(p)

Diffeomorphisms satisfying the specification property

Author(s): Kazuhiro Sakai; Naoya Sumi; Kenichiro Yamamoto
Journal: Proc. Amer. Math. Soc. 138 (2010), 315-321.
MSC (2000): Primary 37A25, 37Bxx, 37C50, 37D20, 37D30
Posted: September 2, 2009
MathSciNet review: 2550197
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Abstract | References | Similar articles | Additional information

Abstract: Let be a diffeomorphism of a closed $C^\infty$ manifold . In this paper, we introduce the notion of the -stable specification property for a closed -invariant set $\Lambda$ of , and we prove that $f_{\vert\Lambda}$ satisfies a -stable specification property if and only if $\Lambda$ is a hyperbolic elementary set. As a corollary, the -interior of the set of diffeomorphisms of satisfying the specification property is characterized as the set of transitive Anosov diffeomorphisms.

References:

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Additional Information:

Kazuhiro Sakai
Affiliation: Department of Mathematics, Utsunomiya University, Utsunomiya 321-8505, Japan
Email: kazsakai@cc.utsunomiya-u.ac.jp

Naoya Sumi
Affiliation: Department of Mathematics, Tokyo Institute of Technology, Tokyo 152-8551, Japan
Email: sumi.n.aa@m.titech.ac.jp

Kenichiro Yamamoto
Affiliation: Department of Mathematics, Tokyo Institute of Technology, Tokyo 152-8551, Japan
Email: yamamoto.k.ak@m.titech.ac.jp

DOI: 10.1090/S0002-9939-09-10085-0
PII: S 0002-9939(09)10085-0
Received by editor(s): February 6, 2009,
Received by editor(s) in revised form: June 24, 2009
Posted: September 2, 2009
Additional Notes: The first author was supported by JSPS Grant-in-Aid for Scientific Research (C) (19540209).
Communicated by: Bryna Kra
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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