NDLI: Non-wandering Sets for Dendrite Maps

Content Provider	Springer Nature Link
Author	Sun, Taixiang He, Qiuli Liu, Jing Tao, Chunyan Xi, Hongjian
Copyright Year	2014
Abstract	Let $$(X,d)$$ be a metric space, and $$f$$ be a continuous map from $$X$$ to $$X$$ , and denote by $$P(f)$$ , $$\omega (f)$$ and $$\Omega (f)$$ the sets of periodic points, $$\omega $$ -limit points and non-wandering points of $$f$$ , respectively. It is well known that for an interval map $$f$$ , the following statements hold: (1) $$\omega (f)=\bigcap _{n=1}^{+\infty }f^n(\Omega (f))$$ . (2) Any isolated point of $$P( f )$$ is also an isolated point of $$\Omega ( f )$$ . (3) $$x\in \Omega ( f )$$ if and only if there exist points $$ x_k\longrightarrow x$$ and positive integers $$n_k\longrightarrow \infty $$ such that $$ f^{ n_k} (x_k) = x$$ . In [Mai and Sun (Topol Appl, 154, 2306–2311, 2007); Mai et al. (J Math Anal Appl, 383, 553–559, 2011)], we generalized those results to graph maps. It is natural to ask whether those results can be generalized to dendrite maps. The aim of this paper is to show that the answer is negative.
Starting Page	101
Ending Page	108
Page Count	8
File Format	PDF
ISSN	15755460
Journal	Qualitative Theory of Dynamical Systems
Volume Number	14
Issue Number	1
e-ISSN	16623592
Language	English
Publisher	Springer Basel
Publisher Date	2014-11-09
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Dendrite map Non-wandering point Periodic point Transformations and group actions with special properties Notions of recurrence Topological dynamics Mathematics Dynamical Systems and Ergodic Theory Difference and Functional Equations
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics Discrete Mathematics and Combinatorics

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