The $C^ 1$ closing lemma for endomorphisms with finitely many singularities
Author:
Lan Wen
Journal:
Proc. Amer. Math. Soc. 114 (1992), 217-223
MSC:
Primary 58F20; Secondary 58F10
DOI:
https://doi.org/10.1090/S0002-9939-1992-1087474-6
MathSciNet review:
1087474
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Abstract | References | Similar Articles | Additional Information
Abstract: The ${C^1}$ closing lemma for endomorphisms with finitely many singularities is obtained by combining the ${C^1}$ closing lemma for nonsingular endomorphisms together with a technique of L. S. Young.
- John Franks, Necessary conditions for stability of diffeomorphisms, Trans. Amer. Math. Soc. 158 (1971), 301β308. MR 283812, DOI https://doi.org/10.1090/S0002-9947-1971-0283812-3
- Shan Tao Liao, An extended $C^{1}$ closing lemma, Beijing Daxue Xuebao 3 (1979), 1β41 (Chinese, with English summary). MR 574171
- Jie Hua Mai, A simpler proof of $C^1$ closing lemma, Sci. Sinica Ser. A 29 (1986), no. 10, 1020β1031. MR 877286 ---, A simpler proof of the extended ${C^1}$ closing lemma, Chinese Sci. Bull. 3 (1989), 180-184.
- Charles C. Pugh, The closing lemma, Amer. J. Math. 89 (1967), 956β1009. MR 226669, DOI https://doi.org/10.2307/2373413
- Charles C. Pugh, An improved closing lemma and a general density theorem, Amer. J. Math. 89 (1967), 1010β1021. MR 226670, DOI https://doi.org/10.2307/2373414
- Charles C. Pugh and Clark Robinson, The $C^{1}$ closing lemma, including Hamiltonians, Ergodic Theory Dynam. Systems 3 (1983), no. 2, 261β313. MR 742228, DOI https://doi.org/10.1017/S0143385700001978
- Clark Robinson, Introduction to the closing lemma, The structure of attractors in dynamical systems (Proc. Conf., North Dakota State Univ., Fargo, N.D., 1977) Lecture Notes in Math., vol. 668, Springer, Berlin, 1978, pp. 225β230. MR 518562
- Lan Wen, A closing lemma for differentiable mappings of the circle, Beijing Daxue Xuebao 2 (1982), 13β22 (Chinese, with English summary). MR 671294 ---, The ${C^1}$ closing lemma of $2$-dimensional non-singular endomorphisms, preprint. ---, The ${C^1}$ closing lemma of non-singular endomorphisms, preprint.
- Lai Sang Young, A closing lemma on the interval, Invent. Math. 54 (1979), no. 2, 179β187. MR 550182, DOI https://doi.org/10.1007/BF01408935
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Article copyright:
© Copyright 1992
American Mathematical Society