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

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.
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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