Dendrite maps whose every periodic point is a fixed point

Taixiang Sun, Qiuli He, Dongwei Su and Hongjian Xi

Chaos, Solitons & Fractals, 2014, vol. 65, issue C, 62-64

Abstract: Let D be a dendrite and f:D⟶D be a continuous map. In this note, we show: (1) Every periodic point of f is a fixed point of f if and only if fn(x) and f(x) are contained in the same connected component of D-{x} for any x∈D with f(x)≠x and any natural number n. (2) If {fn(x)}n=1∞ is convergent for any x∈D, then every periodic point of f is a fixed point of f. Besides, we construct a dendrite D and a continuous map f from D to D which every periodic point is a fixed point but {fn(x)}n=1∞ is not convergent for some x∈D.

Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:65:y:2014:i:c:p:62-64

DOI: 10.1016/j.chaos.2014.04.013

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