The size of the chain recurrent set for generic maps on an n-dimensional locally (n-1)-connected compact space
Katsuya Yokoi
Colloquium Mathematicae, Tome 120 (2010), p. 229-236 / Harvested from The Polish Digital Mathematics Library
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For n ≥ 1, given an n-dimensional locally (n-1)-connected compact space X and a finite Borel measure μ without atoms at isolated points, we prove that for a generic (in the uniform metric) continuous map f:X → X, the set of points which are chain recurrent under f has μ-measure zero. The same is true for n = 0 (skipping the local connectedness assumption).

Publié le : 2010-01-01
EUDML-ID : urn:eudml:doc:284171 
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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 Mathematicae, Tome 120 (2010) pp. 229-236. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm119-2-5/