A short proof of the Birkhoff-Smale theorem
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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
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G. D. Birkhoff, Nouvelles recherches sur les systèmes dynamiques, Collected Mathematical Papers, Vol. 2, Amer. Math. Soc., Providence, R. I., 1950, pp. 530-662.
- Stephen Smale, Diffeomorphisms with many periodic points, Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse), Princeton Univ. Press, Princeton, N.J., 1965, pp. 63–80. MR 0182020
- S. Smale, Differentiable dynamical systems, Bull. Amer. Math. Soc. 73 (1967), 747–817. MR 228014, DOI 10.1090/S0002-9904-1967-11798-1
- J. Palis, On Morse-Smale dynamical systems, Topology 8 (1968), 385–404. MR 246316, DOI 10.1016/0040-9383(69)90024-X
Additional Information
- © Copyright 1985 American Mathematical Society
- 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