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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
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Abstract:
Let  be a diffeomorphism of a closed  manifold  . In this paper, we introduce the notion of the  -stable specification property for a closed  -invariant set  of  , and we prove that  satisfies a  -stable specification property if and only if  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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