Chaos of a sequence of maps in a metric space☆

Tian, Canrong; Chen, Guanrong

doi:10.1016/j.chaos.2005.08.127

Cited by 52 publications

(39 citation statements)

References 4 publications

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“…Similar kind of study related to random perturbations of dynamical systems has been done by Araújo [1]. In [23], introducing many new concepts authors have defined and studied chaos of a time varying map. i.e.…”

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confidence: 95%

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Topological stability of a sequence of maps on a compact metric space

Thakkar

Das

2013

Bull. Math. Sci.

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In this paper we discuss the dynamical system induced by sequence of maps i.e. time varying map on a metric space. We define and study shadowing and expansiveness of such dynamical systems. We show that expansiveness and shadowing of time varying maps are conjugacy invariant. Finally, we prove that a time varying map having shadowing and expansiveness is topologically stable in the class of all time varying maps on a compact metric space.Keywords Expansiveness · Shadowing · Conjugacy · Topological stability Mathematics Subject Classification (2010) Primary 54H20; Secondary 37C75 · 37C15 IntroductionExpansiveness and shadowing are very important and useful dynamical properties of maps on metric spaces. They have lots of applications in Topological dynamics, Ergodic theory, Symbolic dynamics and related areas. One can refer [2,20] for detailed study of these notions. The concept of expansiveness originally introduced for homeomorphisms on metric spaces [24]

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confidence: 95%

“…Definition 2.1 [23] Let (X, d) be a metric space and f n : X → X be a sequence of maps, n = 0, 1, 2, . .…”

Section: For Any I ≤ J We Definementioning

confidence: 99%

Topological stability of a sequence of maps on a compact metric space

Thakkar

Das

2013

Bull. Math. Sci.

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“…[2] : Let (X , d) be a compact metric space and f n : X → X a sequence of continuous functions, n = 1, 2, ··· . If for any two non-empty open subsets U and V of X , there exists a positive integer k such that…”

Section: Sensitive Dependence On Initial Conditions: a Continuous Funmentioning

confidence: 99%

“…In [2], chaos of a time invariant continuous function on a metric space has been extensively studied. The authors also introduced several concepts, such as chaos for a sequence of time invariant functions.…”

Section: Introductionmentioning

confidence: 99%

Uniform convergence and sequence of maps on a compact metric space with some chaotic properties

Bhaumik

Choudhury

2010

Anal. Theory Appl.

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Recently, C. Tain and G. Chen introduced a new concept of sequence of time invariant function. In this paper we try to investigate the chaotic behavior of the uniform limit function f : X → X of a sequence of continuous topologically transitive (in strongly successive way) functions f n : X → X, where X is a compact interval. Surprisingly, we find that the uniform limit function is chaotic in the sense of Devaney. Lastly, we give an example to show that the denseness property of Devaney's definition is lost on the limit function.Key words: uniform convergence, chaos in the sense of Devaney, topological transitivity in strongly successive way

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“…In [6,7], Huang et al studied topological pressure and preimage entropy of nonautonomous discrete systems. In [8][9][10][11][12][13][14][15], authors studied chaos in nonautonomous discrete systems.…”

Section: Introductionmentioning

confidence: 99%