Journal of the Chungcheong Mathematical Society (충청수학회지)
- Volume 13 Issue 1
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- Pages.53-63
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- 2000
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- 1226-3524(pISSN)
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- 2383-6245(eISSN)
TOPOLOGICAL STABILITY OF INVERSE SHADOWING SYSTEMS
- Lee, Keonhee (Department of Mathematics Chungnam National University) ;
- Lee, Joonhee (Department of Mathematics Chungnam National University)
- Received : 2000.05.10
- Published : 2000.06.30
Abstract
The inverse shadowing property of a dynamical system is an "inverse" form of the shadowing property of the system. Recently, Kloeden and Ombach proved that if an expansive system on a compact manifold has the shadowing property then it has the inverse shadowing property. In this paper, we study topological stability of the inverse shadowing dynamical systems. In particular, we show that if an expansive system on a compact manifold has the inverse shadowing property then it is topologically stable, and so it has the shadowing property.
Keywords
- ${\delta}$-method;
- Expansive;
- Inverse shadowing property;
- Inverse shadowing uniqueness property;
- Strongly expansive;
- Shadowing property;
- Shadowing uniqueness property;
- Topologically stable