Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

Closing stable and unstable manifolds on the two sphere


Author: Clark Robinson
Journal: Proc. Amer. Math. Soc. 41 (1973), 299-303
MSC: Primary 58F99
DOI: https://doi.org/10.1090/S0002-9939-1973-0321141-7
MathSciNet review: 0321141
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)

  • [1] R. Abraham and J. Robbin, Transversal mappings and flows, Benjamin, New York, 1967. MR 39 #2181. MR 0240836 (39:2181)
  • [2] G. Choquet, Lectures on analysis. Vol. I, Integration and topological vector spaces, Benjamin, New York, 1969. MR 40 #3252. MR 0250011 (40:3252)
  • [3] J. Palls, A note on $ \Omega $-stability, Proc. Sympos. Pure Math., vol. 14, Amer. Math. Soc., Providence, R.I., 1970, pp. 221-222. MR 42 #5276.
  • [4] C. Pugh, An improved closing lemma and a general density theorem, Amer. J. Math. 89 (1967), 1010-1021. MR 37 #2257. MR 0226670 (37:2257)
  • [5] M. Shub, Stability and genericity for diffeomorphisms, 1971 Brazilian Sympos. on Dynamical Systems, M. Peixoto (editor), Academic Press (to appear). MR 0331431 (48:9764)
  • [6] M. Shub and S. Smale, Beyond hyperbolicity, 1971 Brazilian Sympos. on Dynamical Systems, M. Peixoto (editor), Academic Press (to appear). MR 0312001 (47:563)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58F99

Retrieve articles in all journals with MSC: 58F99


Additional Information

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

American Mathematical Society