The size of the chain recurrent set for generic maps on an n-dimensional locally (n-1)-connected compact space

• Autorzy: Katsuya Yokoi
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 37A05: Measure-preserving transformations
• 37B20: Notions of recurrence
• 37C20: Generic properties, structural stability

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2010
• Tom: 119
• Numer: 2
• Strony: 229-236

Daty

wydano

2010

Twórcy

autor

Katsuya Yokoi

• Department of Mathematics, Shimane University at Matsue, Matsue, 690-8504, Japan
• Department of Mathematics, Jikei University School of Medicine, Chofu, Tokyo 182-8570, Japan

Identyfikatory

DOI

10.4064/cm119-2-5