## Infinitesimally stable endomorphisms

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- by Hiroshi Ikeda PDF
- Trans. Amer. Math. Soc.
**344**(1994), 823-833 Request permission

## Abstract:

It is well known that infinitesimal stability of diffeomorphisms is an open property. However, infinitesimal stability of endomorphisms is not an open property. So we consider the interior of the set of all infinitesimally stable endomorphisms. We prove that if*f*belongs to the interior of the set of all infinitesimally stable endomorphisms, then

*f*is $\Omega$-stable. This means a generalization of Smale’s $\Omega$-stability theorem for diffeomorphisms. Moreover, it is proved that for Anosov endomorphisms structural stability is equivalent to lying in the interior of the set of infinitesimally stable endomorphisms.

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## Additional Information

- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**344**(1994), 823-833 - MSC: Primary 58F10; Secondary 58F15
- DOI: https://doi.org/10.1090/S0002-9947-1994-1250821-2
- MathSciNet review: 1250821