On -limit sets of non-autonomous discrete systems on trees

✍ Scribed by Taixiang Sun

• Publisher: Elsevier Science
• Year: 2008
• Tongue: English
• Weight: 159 KB
• Volume: 68
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2006.11.035

✦ Synopsis

Let T be a tree and f n be a sequence of continuous maps from T to T which converges uniformly to a continuous map f . In this note we show that if every periodic point of f is a fixed point, then for every x ∈ T , ω(x, f n ), ω-limit set of x under (T, f n ), is a closed connected subset of T and every point of ω(x, f n ) is a fixed point of f .