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)

 
 

 

A short proof of the Birkhoff-Smale theorem


Author: T. Mrowka
Journal: Proc. Amer. Math. Soc. 93 (1985), 377-378
MSC: Primary 58F15; Secondary 34C35, 58F20
DOI: https://doi.org/10.1090/S0002-9939-1985-0770559-5
MathSciNet review: 770559
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A short proof of the Birkhoff-Smale theorem on homoclinic points of diffeomorphisms is given. The proof is elementary in that only the local properties of a hyperbolic fixed point are assumed.


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

  • [1] G. D. Birkhoff, Nouvelles recherches sur les systèmes dynamiques, Collected Mathematical Papers, Vol. 2, Amer. Math. Soc., Providence, R. I., 1950, pp. 530-662.
  • [2] S. Smale, Diffeomorphisms with many periodic points, Differential and Combinatorial Topology, Princeton Univ. Press, Princeton, N. J., 1965, pp. 63-80. MR 0182020 (31:6244)
  • [3] -, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747-817. MR 0228014 (37:3598)
  • [4] J. Pahs, On Morse-Smale dynamical systems, Topology 8 (1969), 385-405. MR 0246316 (39:7620)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 58F15, 34C35, 58F20

Retrieve articles in all journals with MSC: 58F15, 34C35, 58F20


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1985-0770559-5
Keywords: Birkhoff-Smale theorem, homoclinic point, periodic point, dynamical systems
Article copyright: © Copyright 1985 American Mathematical Society

American Mathematical Society