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Le "Closing lemma" en topologie C1

Marie-Claude Arnaud

出版	Société mathématique de France, 1998
ISBN	285629071X9782856290712
URL	http://books.google.com.hk/books?id=UI92QgAACAAJ&hl=&source=gbs_api

註釋

Using an algebraic result due to Mai, Arnaud gives a simpler proof of the $C^1$ closing lemma of Pugh and Robinson and gives a more precise result. A new case is solved: the case of symplectic vector fields. The theorem of density of periodic points in the non-wandering set is deduced, as Pugh and Robinson did, adding a result on symplectic vector fields. Then, a new result is proven: the $C^1$ orbit closing lemma, which allows for transforming a recurrent point to a periodic one by approximating its orbit. Arnaud gives a generalization of the ergodic version of the closing lemma of R. Mane to the case of non-compact manifolds and positive Borel measures which are finite on compacta.