The C 1 closing lemma for generic C 1 endomorphisms
Rovella, Alvaro ; Sambarino, Martín
Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010), p. 1461-1469 / Harvested from Numdam
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Given a compact m-dimensional manifold M and 1⩽r⩽∞, consider the space C r (M) of self mappings of M. We prove here that for every map f in a residual subset of C 1 (M), the C 1 closing lemma holds. In particular, it follows that the set of periodic points is dense in the nonwandering set of a generic C 1 map. The proof is based on a geometric result asserting that for generic C r maps the future orbit of every point in M visits the critical set at most m times.

Publié le : 2010-01-01
DOI : https://doi.org/10.1016/j.anihpc.2010.09.003
Classification:  37Cxx,  58K05 
@article{AIHPC_2010__27_6_1461_0,
     author = {Rovella, Alvaro and Sambarino, Mart\'\i n},
     title = {The $ {C}^{1}$ closing lemma for generic $ {C}^{1}$ endomorphisms},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     volume = {27},
     year = {2010},
     pages = {1461-1469},
     doi = {10.1016/j.anihpc.2010.09.003},
     mrnumber = {2738328},
     zbl = {1214.37009},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIHPC_2010__27_6_1461_0}
}

Rovella, Alvaro; Sambarino, Martín. The $ {C}^{1}$ closing lemma for generic $ {C}^{1}$ endomorphisms. Annales de l'I.H.P. Analyse non linéaire, Tome 27 (2010) pp. 1461-1469. doi : 10.1016/j.anihpc.2010.09.003. http://gdmltest.u-ga.fr/item/AIHPC_2010__27_6_1461_0/

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