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The C1 closing lemma for non-singular endomorphisms†

Published online by Cambridge University Press:  19 September 2008

Lan Wen
Lan Wen
Affiliation:
Department of Mathematics, Peking University, Beijing, 100871, China
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Abstract

A slightly improved version of the (idealized) C1 closing lemma is proved. This turns out to generalize the C1 closing lemma from diffeomorphisms to nonsingular endomorphisms.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 11 , Issue 2 , June 1991 , pp. 393 - 412
Copyright
Copyright © Cambridge University Press 1991

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References

REFERENCES

[1]Franks, J.. Necessary conditions for stability of diffeomorphisms. Trans. Amer. Math. Soc. 158 (1971), 301–308.Google Scholar
[2]Liao, S. T.. An extension of the C 1 closing lemma. Acta Scientiarum Naturalium Universitatis Pekinensis 3 (1979), 1–14 (in Chinese).Google Scholar
[3]Mai, J.. A simpler proof ofC 1 closing lemma. Scientia Sinica (Series A). XXIX (10) (1986), 1021–1031.Google Scholar
[4]Mai, J.. A simpler proof of the extended C 1 closing lemma. Chinese Sci. Bull. 3 (1989), 180–184.Google Scholar
[5]Pugh, C.. The closing lemma. Amer. J. Math. 89 (1967), 956–1009.Google Scholar
[6]Pugh, C.. An improved closing lemma and a general density theorem. Amer. J. Math. 89 (1967), 1010–1021.CrossRefGoogle Scholar
[7]Pugh, C. & Robinson, C.. The C 1 closing lemma, including Hamiltonians. Ergod. Th. & Dynam. Sys. 3 (1983), 261–313.CrossRefGoogle Scholar
[8]Robinson, C.. Introduction to the closing lemma. Springer Lecture Notes in Math. 668 (1978) pp. 223–230.Google Scholar
[9]Wen, L.. The C 1 closing lemma of 2-dimensional non-singular endomorphisms. Preprint.Google Scholar
[10]Wen, L.. The C 1 closing lemma for endomorphisms with finitely many singularities. Proc. Amer. Math. Soc., to appear.Google Scholar