Mean chain transitivity and almost mean shadowing property of iterated function systems

Thiyam Thadoi Devi; Khundrakpam Binod Mangang; Sonika Akoijam; Lalhmangaihzuala; Phinao Ramwungzan; Jay Prakash Singh; Thiyam Thadoi Devi; Khundrakpam Binod Mangang; Sonika Akoijam; Lalhmangaihzuala; Phinao Ramwungzan; Jay Prakash Singh

doi:10.3934/math.20241012

AIMS Mathematics

2024, Volume 9, Issue 8: 20811-20825. doi: 10.3934/math.20241012

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Research article

Mean chain transitivity and almost mean shadowing property of iterated function systems

1.
Department of Mathematics, Manipur University, Canchipur, Imphal, Manipur 795003, India
2.
Department of Mathematics, Government Serchhip College, Serchhip, Mizoram 796181, India
3.
Department of Mathematics, Manipur Technical University, Imphal, Manipur 795004, India
4.
Department of Mathematics, Central University of South Bihar, Gaya, Bihar 824236, India

Received: 03 May 2024 Revised: 18 June 2024 Accepted: 21 June 2024 Published: 27 June 2024
MSC : 37B65, 37B99, 26A18

In this paper, we introduce the notions of mean chain transitivity, mean chain mixing, totally mean chain transitivity, and almost mean shadowing property to iterated function systems (IFS). We study the interrelations of these notions. We prove that an iterated function system is chain transitive if one of the constituent maps is surjective, and it has almost mean shadowing property.
- transitivity,
- shadowing,
- pseudo-orbits,
- chains,
- iterated function systems
Citation: Thiyam Thadoi Devi, Khundrakpam Binod Mangang, Sonika Akoijam, Lalhmangaihzuala, Phinao Ramwungzan, Jay Prakash Singh. Mean chain transitivity and almost mean shadowing property of iterated function systems[J]. AIMS Mathematics, 2024, 9(8): 20811-20825. doi: 10.3934/math.20241012

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Abstract

In this paper, we introduce the notions of mean chain transitivity, mean chain mixing, totally mean chain transitivity, and almost mean shadowing property to iterated function systems (IFS). We study the interrelations of these notions. We prove that an iterated function system is chain transitive if one of the constituent maps is surjective, and it has almost mean shadowing property.

References

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