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Closing stable and unstable manifolds on the two sphere


Author: Clark Robinson
Journal: Proc. Amer. Math. Soc. 41 (1973), 299-303
MSC: Primary 58F99
MathSciNet review: 0321141
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Abstract: Let $ f$ be a diffeomorphism of the two sphere. In this note we prove that if the unstable manifold of a fixed point $ p$ for $ f$ accumulates on the stable manifold of $ p$, then $ f$ can be approximated arbitrarily closely $ {C^r},r \geqq 1$, such that they intersect.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0321141-7
Article copyright: © Copyright 1973 American Mathematical Society