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Hyperbolic manifolds with the strongly shadowing property

Published online by Cambridge University Press:  17 April 2009

Keon-Hee Lee  and
Jong-Myung Kim
Keon-Hee Lee
Affiliation:
Department of MathematicsChungnam National UniversityTaejon 305–764Korea e-mail: khlee@math.chungnam.ac.kr
Jong-Myung Kim
Affiliation:
Department of Mathematics EducationKwandong UniversityKangnung210–701Korea
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Abstract

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Let f be a C1 diffeomorphism of a compact smooth manifold M and λ ⊂ M a C1 compact invariant submanifold with a hyperbolic structure as a subset of M. We show that the diffeomorphism | λ is Anosov if and only if λ has the strongly shadowing property, and find hyperbolic sets which have the strongly shadowing property.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 60 , Issue 1 , August 1999 , pp. 37 - 43
Copyright
Copyright © Australian Mathematical Society 1999

References

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