Some stronger forms of topological transitivity and sensitivity for a sequence of uniformly convergent continuous maps

Li, Risong; Lu, Tianxiu; Chen, Guanrong

doi:10.1016/j.jmaa.2020.124443

Cited by 10 publications

(3 citation statements)

References 22 publications

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“…For any initial value x 0 ∈ H, the orbit of [4,5] if for any nonempty open subset V of H, int( f n (V)) = φ for any n ∈ N. Where intA denotes the interior of set A.…”

Section: Preliminariesmentioning

confidence: 99%

“…Li, Zhao, and Wang [4] studied stronger forms of sensitivity and transitivity for NDDS by using the Furstenberg family. Meanwhile, under the condition lim n→∞ d ∞ (g m m , g m ) = 0, a necessary and sufficient condition for g to be F -mixing is established in [5]. Vasisht and Das [6] discussed the difference between F -sensitivity and some other stronger forms of sensitivity by some examples.…”

Section: Introductionmentioning

confidence: 99%

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Sensitivity of Uniformly Convergent Mapping Sequences in Non-Autonomous Discrete Dynamical Systems

Jiang

Yang

2022

Fractal Fract

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Let H be a compact metric space. The metric of H is denoted by d. And let (H,f1,∞) be a non-autonomous discrete system where f1,∞={fn}n=1∞ is a mapping sequence. This paper discusses infinite sensitivity, m-sensitivity, and m-cofinitely sensitivity of f1,∞. It is proved that, if fn(n∈N) are feebly open and uniformly converge to f:H→H, fi∘f=f∘fi for any i∈{1,2,…}, and ∑i=1∞D(fi,f)<∞, then (H,f) has the above sensitive property if and only if (H,f1,∞) has the same property where D(·,·) is the supremum metric.

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“…For any initial value x 0 ∈ H, the orbit of [4,5] if for any nonempty open subset V of H, int( f n (V)) = φ for any n ∈ N. Where intA denotes the interior of set A.…”

Section: Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Sensitivity of Uniformly Convergent Mapping Sequences in Non-Autonomous Discrete Dynamical Systems

Jiang

Yang

2022

Fractal Fract

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“…So, when is a system sensitive? This question has gained some attention in more recent papers (see [10,[13][14][15][16]). A TDS ðW, hÞ is sensitive if for any region E of the phase space W there are two points in E and some s ∈ f0, 1,⋯g satisfying that the sth iterate of the two points under the map h is significantly separated.…”

Section: Introductionmentioning

confidence: 99%

Three Types of Distributional Chaos for a Sequence of Uniformly Convergent Continuous Maps

et al. 2022

Advances in Mathematical Physics

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Let h s s = 1 ∞ be a sequence of continuous maps on a compact metric space W which converges uniformly to a continuous map h on W . In this paper, some equivalence conditions or necessary conditions for the limit map h to be distributional chaotic are obtained (where distributional chaoticity includes distributional chaotic in a sequence, distributional chaos of type 1 (DC1), distributional chaos of type 2 (DC2), and distributional chaos of type 3 (DC3)).

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Mean Li-Yorke Chaos and Mean Sensitivity in Non-autonomous Discrete Systems

Yin

Chen

2022

J Dyn Control Syst

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Some stronger forms of topological transitivity and sensitivity for a sequence of uniformly convergent continuous maps

Cited by 10 publications

References 22 publications

Sensitivity of Uniformly Convergent Mapping Sequences in Non-Autonomous Discrete Dynamical Systems

Sensitivity of Uniformly Convergent Mapping Sequences in Non-Autonomous Discrete Dynamical Systems

Three Types of Distributional Chaos for a Sequence of Uniformly Convergent Continuous Maps

Mean Li-Yorke Chaos and Mean Sensitivity in Non-autonomous Discrete Systems

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