The Chain Properties and Average Shadowing Property of Iterated Function Systems

2016 ◽  
Vol 17 (1) ◽  
pp. 219-227 ◽  
Author(s):  
Xinxing Wu ◽  
Lidong Wang ◽  
Jianhua Liang
Keyword(s):  
Iterated Function Systems ◽  
Shadowing Property ◽  
Iterated Function

Shadowing and average shadowing properties for iterated function systems

2015 ◽  
Vol 22 (2) ◽  
Author(s):  
Alireza Zamani Bahabadi
Keyword(s):  
Iterated Function System ◽  
Iterated Function Systems ◽  
Function System ◽  
Skew Product ◽  
Shadowing Property ◽  
Iterated Function ◽  
Chain Transitivity

AbstractIn this paper, we introduce the definitions of shadowing and average shadowing properties for iterated function systems and give some examples characterizing these definitions. We prove that an iterated function system has the shadowing property if and only if the step skew product corresponding to the iterated function system has the shadowing property. Also, we study some notions such as transitivity, chain transitivity, chain mixing and mixing for iterated function systems.

scholarly journals Variants of shadowing properties for iterated function systems on uniform spaces

Filomat ◽  
2021 ◽  
Vol 35 (8) ◽  
pp. 2565-2572
Author(s):  
Radhika Vasisht ◽  
Mohammad Salman ◽  
Ruchi Das
Keyword(s):  
Iterated Function System ◽  
Iterated Function Systems ◽  
Function System ◽  
Uniform Spaces ◽  
Shadowing Property ◽  
Topological Mixing ◽  
Topologically Transitive ◽  
Iterated Function ◽  
Chain Transitivity

In this paper, the notions of topological shadowing, topological ergodic shadowing, topological chain transitivity and topological chain mixing are introduced and studied for an iterated function system (IFS) on uniform spaces. It is proved that if an IFS has topological shadowing property and is topological chain mixing, then it has topological ergodic shadowing and it is topological mixing. Moreover, if an IFS has topological shadowing property and is topological chain transitive, then it is topologically ergodic and hence topologically transitive. Also, these notions are studied for the product IFS on uniform spaces.

scholarly journals Two-Sided Limit Shadowing Property on Iterated Function Systems

2020 ◽  
Vol 44 (1) ◽  
pp. 113-125 ◽  
Author(s):  
M. MOHTASHAMIPOUR ◽  
◽  
A. ZAMANI BAHABADI
Keyword(s):  
Iterated Function Systems ◽  
Shadowing Property ◽  
Iterated Function ◽  
Limit Shadowing

Periodic shadowing in iterated function systems

2021 ◽  
pp. 2250064
Author(s):  
Ali Darabi
Keyword(s):  
Iterated Function Systems ◽  
Shadowing Property ◽  
Iterated Function

In this paper, we introduce the notion of periodic shadowing property on iterated function systems, IFSs for short, and then some results will be obtained and compare with similar ones in the references. Among those results, we prove that every strongly expansive IFS with the shadowing property has the periodic shadowing property. In addition, like the shadowing property, we show that every uniformly expanding IFS has the periodic shadowing property. However, the periodic shadowing property is fulfilled for the uniformly contracting IFS provided that it is expansive.

Shadowing property and topological ergodicity for iterated function systems

2019 ◽  
Vol 33 (23) ◽  
pp. 1950272
Author(s):  
Yingcui Zhao ◽  
Lidong Wang ◽  
Fengchun Lei
Keyword(s):  
Metric Space ◽  
Iterated Function System ◽  
Iterated Function Systems ◽  
Function System ◽  
Skew Product ◽  
Semi Group ◽  
Compact Metric Space ◽  
Shadowing Property ◽  
Iterated Function ◽  
Continuous Maps

Let [Formula: see text] be a compact metric space and [Formula: see text] be two continuous maps on [Formula: see text]. The iterated function system [Formula: see text] is the action of the semi-group generated by [Formula: see text] on [Formula: see text]. In this paper, we introduce the definitions of shadowing property, average shadowing property and topological ergodicity for [Formula: see text] and give some examples. Then we show that (1) if [Formula: see text] has the shadowing property then so do [Formula: see text] and [Formula: see text]; (2) [Formula: see text] has the shadowing property if and only if the step skew product corresponding to [Formula: see text] has the shadowing property. At last, we prove a Lyapunov stable iterated function system having the average shadowing property is topologically ergodic.

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