Nonwandering points of monotone local dendrite maps revisited

Abdelli, Hafedh; Abouda, Haithem; Marzougui, Habib

doi:10.1016/j.topol.2018.10.005

Cited by 9 publications

(4 citation statements)

References 20 publications

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“…− for homeomorphisms on regular curves (Naghmouchi [29]) − for monotone maps on local dendrites (Abdelli et al [3]) In Theorem 3.1, we prove a more general result by showing that this is true for monotone maps on regular curves. Nevertheless, the later result is false in general for monotone maps on dendroids as it is shown in Example 3.5.…”

Section: Introductionmentioning

confidence: 91%

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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: Introductionmentioning

confidence: 91%

“…In the last two decades, a wide literature on the dynamical properties of maps on some one-dimensional continua has developed. Examples of continua become increasingly studied include, graphs, dendrites and local dendrites (see for instance [1], [2], [3], [30]).…”

Section: Introductionmentioning

confidence: 99%

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

Daghar¹,

Marzougui²

2021

Preprint

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“…This was proved in two cases: − for homeomorphisms on regular curves (Naghmouchi [19]) − for monotone maps on local dendrites (Abdelli et al [3])…”

Section: Preliminariesmentioning

confidence: 99%

“…In the last two decades, the study of dynamical systems in one dimensional continua has developed and become increasingly intensive due to the rich dynamical properties that one dimensional maps can exhibit. Examples of continua studied include, graphs, dendrites and local dendrites (see for instance [1], [2], [3], [20]). Recently regular curves has given a special attention (see for example, [4], [10], [11], [18], [19], [21]).…”

Section: Introductionmentioning

confidence: 99%

On Limit sets of Monotone maps on Regular curves

Daghar¹,

Marzougui²

2021

Preprint

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We investigate the structure of ω-limit (resp. α-limit) sets for a monotone map f on a regular curve X. We show that for any x ∈ X (resp. for any negative orbit (xn) n≥0 of x), the ω-limit set ω f (x) (resp. α-limit set α f ((xn) n≥0 )) is a minimal set. This also hold for α-limit set α f (x) whenever x is not a periodic point. These results extend those of Naghmouchi [18] established whenever f is a homeomorphism on a regular curve and those of Abdelli [1] , whenever f is a monotone map on a local dendrite. Further results related to the basin of attraction of an infinite minimal set are also obtained.

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Nonwandering Sets and Special $$\alpha $$-limit Sets of Monotone Maps on Regular Curves

Daghar¹,

Marzougui²

2023

Springer Proceedings in Mathematics &Amp; Statistics

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Nonwandering points of monotone local dendrite maps revisited

Cited by 9 publications

References 20 publications

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

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

On Limit sets of Monotone maps on Regular curves

Nonwandering Sets and Special $$\alpha $$-limit Sets of Monotone Maps on Regular Curves

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