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【期刊论文】A CHAOTIC MAP WITH TOPOLOGICAL ENTROPY
熊金城, Xiong Jincheng
Acta Mathematica Scientia 6 (1986), 4, 439-443,-0001,():
-1年11月30日
An interval map with topologyical entropy 0 may be chaotic.
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【期刊论文】The attracting centre of a continuous self-map of the interval
熊金城, XIONG JINCHENG
Ergod. Th. & Dynam. Sys. (1988), 8, 205-213 Printed in Great Britain,-0001,():
-1年11月30日
Let f denote a continuous map of a compact interval I to itself. A point x∈I is called a γ-limit point of f if it is both an ω-limit point and a α-limit point of some point y∈I. Let I’denote the set of γ-limit points. In the present paper, we show that (1) P-I’ is either empty or countably infinite, where P denotes the closure of the set P of periodic points, (2) x∈I is a γ-limit point if and only if there exist y1 and y2 in I such that x is an ω-limit points of y1, and y1 is an ω-limit point of y2, and if and only if there exists a sequence y1, y2, … of points in I such that x is an ω-limit point of y1, and y1 is an ω-limit point of yi+1 for every i≥1, and (3) the period of each periodic point of f is a power of 2 if and only if every γ-limit point is recurrent.
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