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On the product of stable diffeomorphisms


Author: Atsuro Sannami
Journal: Proc. Amer. Math. Soc. 88 (1983), 545-549
MSC: Primary 58F10; Secondary 58F15
DOI: https://doi.org/10.1090/S0002-9939-1983-0699431-4
MathSciNet review: 699431
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Abstract: It is proved that statements (a)-(c) are equivalent, (a) Structural $ (\Omega - )$ stability conjecture. (b) If diffeomorphisms $ f$ and $ g$ are both structurally $ (\Omega - )$ stable, then so is $ f \times g$. (c) If a diffeomorphism $ f$ is structurally $ (\Omega - )$ stable, then every diffeomorphism in a neighborhood of $ f \times {f^{ - 1}}$ has only hyperbolic periodic points.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1983-0699431-4
Article copyright: © Copyright 1983 American Mathematical Society