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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On stability of endomorphisms


Author: Hiroshi Ikeda
Journal: Proc. Amer. Math. Soc. 104 (1988), 1287-1290
MSC: Primary 58F10
MathSciNet review: 941323
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Abstract: In this note we prove a generalization of R. Mañé's theorem. R. Mañé proved that $ {C^r}$ absolutely stable endomorphisms satisfy Axiom A. We prove that if an endomorphism $ f$ is both $ {C^r}$ structurally and infinitesimally stable, then $ f$ satisfies Axiom A.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1988-0941323-1
PII: S 0002-9939(1988)0941323-1
Keywords: Infinitesimal stability, Axiom A, prehyperbolic set, $ \bar P$-stability
Article copyright: © Copyright 1988 American Mathematical Society