Pointwise chain recurrent maps of the space Y

• Published in: Bulletin of the Australian Mathematical Society Vol. 67; no. 1; pp. 79 - 85
• Main Authors: Guo, Wenjing, Zeng, Fanping, Hu, Qiying
• Format: Journal Article
• Language: English
• Published: Cambridge, UK Cambridge University Press 01.02.2003
• Subjects: Chains; Topology
• ISSN: 0004-9727; 1755-1633
• DOI: 10.1017/S0004972700033530

Let Y = {z ∈ C: z3 ∈ [0, 1]} (equipped with subspace topology of the complex space C) and let f: Y → Y be a continuous map. We show that if f is pointwise chain recurrent (that is, every point of Y is chain recurrent under f), then either f12 is the identity map or f12 is turbulent. This result is a generalisation to Y of a result of Block and Coven for pointwise chain recurrent maps of the interval.