The planar closing lemma for chain recurrence
HTML articles powered by AMS MathViewer
- by Maria Lúcia Alvarenga Peixoto and Charles Chapman Pugh PDF
- Trans. Amer. Math. Soc. 341 (1994), 173-192 Request permission
Abstract:
If $z$ is a chain recurrent point of a ${C^r}$ planar flow, all of whose fixed points are hyperbolic, then it is proved that the orbit through $z$ becomes periodic under a perturbation that is ${C^r}$ small in the Whitney topology.References
- N. P. Bhatia and G. P. Szegö, Stability theory of dynamical systems, Die Grundlehren der mathematischen Wissenschaften, Band 161, Springer-Verlag, New York-Berlin, 1970. MR 0289890
- Zbigniew Nitecki, Explosions in completely unstable flows. I. Preventing explosions, Trans. Amer. Math. Soc. 245 (1978), 43–61. MR 511399, DOI 10.1090/S0002-9947-1978-0511399-2
- Maria Lúcia Alvarenga Peixoto, The closing lemma for generalized recurrence in the plane, Trans. Amer. Math. Soc. 308 (1988), no. 1, 143–158. MR 946436, DOI 10.1090/S0002-9947-1988-0946436-0
- Charles C. Pugh, The closing lemma, Amer. J. Math. 89 (1967), 956–1009. MR 226669, DOI 10.2307/2373413
- Charles C. Pugh, An improved closing lemma and a general density theorem, Amer. J. Math. 89 (1967), 1010–1021. MR 226670, DOI 10.2307/2373414
- Charles Pugh, Against the $C^{2}$ closing lemma, J. Differential Equations 17 (1975), 435–443. MR 368079, DOI 10.1016/0022-0396(75)90054-6 —, The ${C^1}$-connecting lemma, a counterexample (preprint), 1984.
Additional Information
- © Copyright 1994 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 341 (1994), 173-192
- MSC: Primary 58F30; Secondary 58F20, 58F25
- DOI: https://doi.org/10.1090/S0002-9947-1994-1107028-9
- MathSciNet review: 1107028