The oe-property of diffeomorphisms

Kazuhiro Sakai

doi:10.3934/dcds.1998.4.581

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1998, Volume 4, Issue 3: 581-591. Doi: 10.3934/dcds.1998.4.581

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The oe-property of diffeomorphisms

Kazuhiro Sakai^1,

1.
Department of Mathematics, Kanagawa University, Rokkakubashi, Kanagawa-ku, Yokohama 221

Received: May 1997

Revised: November 1997

Published: July 1998

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Abstract

In this paper, the $C^1$ interior of the set of all diffeomorphisms satisfying the OE-property is characterized as the set of all diffeomorphisms satisfying Axiom A and the strong transversality condition. Thus the $C^1$ interior of the set of all diffeomorphisms satisfying the OE-property is equal to the $C^1$ interior of the set of all diffeomorphisms satisfying the shadowing property.

Keywords:

Extended orbits,
pseudo-orbits,
Axiom A and strong transversality condition,
shadowing property,
structurally stable.

Mathematics Subject Classification: 54H20, 58F10, 58F15.

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