Non-wandering Sets for Dendrite Maps

Sun, Taixiang; Liu, Jing; Tao, Chunyan; Xi, Hongjian

doi:10.1007/s12346-014-0127-7

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Nonwandering Sets Of Monotone Maps On Regular Curves1

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2017

2023

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Cited by 5 publications

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“…Later, it is extended to graph maps in [26, Corollary 1]. However, for dendrite maps, it does not holds (see [32]). The following theorem extend the above result to monotone maps on regular curves.…”

Section: Nonwandering Sets Of Monotone Maps On Regular Curvesmentioning

confidence: 99%

Nonwandering sets and special $α$-limit sets of monotone maps on regular curves

Daghar¹,

Marzougui²

2021

Preprint

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Let X be a regular curve and let f : X → X be a monotone map. In this paper, nonwandering set of f and the structure of special α-limit sets for f are investigated. We show that AP(f ) = R(f ) = Ω(f ), where AP(f ), R(f ) and Ω(f ) are the sets of almost periodic points, recurrent points and nonwandering of f , respectively. This result extends that of Naghmouchi established, whenever f is a homeomorphism on a regular curve [

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Section: Nonwandering Sets Of Monotone Maps On Regular Curvesmentioning

confidence: 99%