Geodesic
The size of the chain recurrent set for generic maps on an $n$-dimensional locally $(n-1)$-connected compact space
Katsuya Yokoi1
1 Department of Mathematics Shimane University at Matsue Matsue, 690-8504, Japan and Department of Mathematics Jikei University School of Medicine Chofu, Tokyo 182-8570, Japan
Colloquium Mathematicum, Tome 119 (2010) no. 2, pp. 229-236.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

For $n \geq 1$, given an $n$-dimensional locally $(n-1)$-connected compact space $X$ and a finite Borel measure $\mu$ without atoms at isolated points, we prove that for a generic (in the uniform metric) continuous map $f:X \to X$, the set of points which are chain recurrent under $f$ has $\mu$-measure zero. The same is true for $n =0$ (skipping the local connectedness assumption).
DOI : 10.4064/cm119-2-5
Keywords: geq given n dimensional locally n connected compact space finite borel measure without atoms isolated points prove generic uniform metric continuous map set points which chain recurrent under has mu measure zero skipping local connectedness assumption

Katsuya Yokoi 1

1 Department of Mathematics Shimane University at Matsue Matsue, 690-8504, Japan and Department of Mathematics Jikei University School of Medicine Chofu, Tokyo 182-8570, Japan 
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Katsuya Yokoi. The size of the chain recurrent set
for generic maps
on an $n$-dimensional locally $(n-1)$-connected compact space. Colloquium Mathematicum, Tome 119 (2010) no. 2, pp. 229-236. doi : 10.4064/cm119-2-5. http://geodesic.mathdoc.fr/articles/10.4064/cm119-2-5/

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