The oe-property of diffeomorphisms

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July 1998, 4(3): 581-591. doi: 10.3934/dcds.1998.4.581

The oe-property of diffeomorphisms

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

Received May 1997 Revised November 1997 Published April 1998

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

Mathematics Subject Classification: 54H20, 58F10, 58F1.

Citation: Kazuhiro Sakai. The oe-property of diffeomorphisms. Discrete & Continuous Dynamical Systems - A, 1998, 4 (3) : 581-591. doi: 10.3934/dcds.1998.4.581

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