The Strong <i>G</i>-shadowing Property of the Inverse Limit Spaces and the Product Spaces of Group Action

JI Zhanjiang; ZHANG Gengrong; TU Jingxian

doi:10.6054/j.jscnun.2019108

Journal of South China Normal University (Natural Science Edition) > 2019 > 51(6): 103-106. > DOI: 10.6054/j.jscnun.2019108

JI Zhanjiang, ZHANG Gengrong, TU Jingxian. The Strong G-shadowing Property of the Inverse Limit Spaces and the Product Spaces of Group Action[J]. Journal of South China Normal University (Natural Science Edition), 2019, 51(6): 103-106. DOI: 10.6054/j.jscnun.2019108

Citation:

PDF (409 KB)

The Strong G-shadowing Property of the Inverse Limit Spaces and the Product Spaces of Group Action

1.
School of Data Science and Software Engineering//Guangxi Colleges and Universities Key Laboratory of Image Processing and Intelligent Information System, Wuzhou University, Wuzhou 543002, China
2.
School of Mathematics and Computational Science, Hunan First Normal University, Changsha 410205, China

More Information

Received Date: January 01, 2019
Available Online: March 21, 2021

Graphical Abstract

Abstract

Abstract

The concept of the strong G-shadowing property is given in the metric spaces under the action of topologi-cal group. Then the dynamical properties of the strong G-shadowing property in the inverse limit spaces and the product spaces under the action of topological group are studied. The following conclusions are obtained. Let the system (X_f, G, d, σ) be the inverse limit spaces of the system (X, G, d, f). Then f has the G-shadowing property if and only if σ has the G-shadowing property. The product map f₁×f₂ has the strong G-shadowing property if and only if the map f₁ has the strong G₁-shadowing property and the map f₂ has the strong G₂-shadowing property. These results enrich the theory of strong G-shadowing property in the inverse limit spaces and the product spaces under the action of topological group.
- G-shadowing property,
- strong G-shadowing property,
- inverse limit spaces,
- product spaces

FullText(HTML)

References (15)

References

[1]	NIU Y X. The average-shadowing property and strong ergodicity[J]. Journal of Mathematical Analysis and Applications, 2011, 376(2):528-534. doi: 10.1016/j.jmaa.2010.11.024
[2]	汪火云, 曾鹏.平均伪轨的部分跟踪[J].中国科学:数学, 2016, 46(4):781-792. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=zgkx-ca201606002 WANG H Y, ZENG P. Partial shadowing of average pseudo-orbits[J]. Scientific Sinica:Mathematica, 2016, 46(4):781-792. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=zgkx-ca201606002
[3]	顾荣宝, 盛业青.关于渐近的伪轨跟踪性质[J].安徽大学学报(自然科学版), 2003, 27(3):1-5. doi: 10.3969/j.issn.1000-2162.2003.03.001 GU R B, SHENG Y Q. On the asymptotic pseudo orbit tracing property[J]. Journal of Anhui University(Natural Science Edition), 2003, 27(3):1-5. doi: 10.3969/j.issn.1000-2162.2003.03.001
[4]	晏炳刚, 吴泽刚.关于强跟踪性的注记[J].成都大学学报(自然科学版), 2007, 26(4):292-294. doi: 10.3969/j.issn.1004-5422.2007.04.009 YAN B G, WU Z G. Notes about strong shadowing property[J]. Journal of Chengdu University(Natural Science Edition), 2007, 26(4):292-294. doi: 10.3969/j.issn.1004-5422.2007.04.009
[5]	赵俊玲, 张莉.周期伪轨跟踪性和伪轨跟踪性的关系[J].浙江大学学报(理学版), 2010, 37(5):505-507. doi: 10.3785/j.issn.1008-9497.2010.05.005 ZHAO J L, ZHANG L. Relationship between the periodic pseudo orbit tracing property and the pseudo orbit tracing property[J]. Journal of Zhejiang University(Science Edition), 2010, 37(5):505-507. doi: 10.3785/j.issn.1008-9497.2010.05.005
[6]	GU R B, SHENG Y Q. APOTP for the inverse limit spaces[J]. Applied Mathematics Journal, 2006, 21(4):473-478. doi: 10.1007/s11766-006-0012-5
[7]	朱玉峻, 何连法.线性系统的极限跟踪性[J].数学物理学报, 2007, 27(2):314-321. doi: 10.3321/j.issn:1003-3998.2007.02.016 ZHU Y J, HE L F. Limit shadowing property of linear systems[J]. Acta Mathematica Scientia, 2007, 27(2):314-321. doi: 10.3321/j.issn:1003-3998.2007.02.016
[8]	HOSSEIN R. On the shadowing property of nonautonomous discrete systems[J]. International Journal of Nonlinear Analysis and Applications, 2016(1):271-277. http://cn.bing.com/academic/profile?id=9325b0f910c9daa3b898235df5be42cb&encoded=0&v=paper_preview&mkt=zh-cn
[9]	HOSSEIN R, REZA M. On the relation of shadowing and expansivity in nonautonomous discrete systems[J]. Analy-sis in Theory and Applications, 2017, 33(1):11-19. doi: 10.4208/ata.2017.v33.n1.2
[10]	FAKHARI A, GHANE F H. On shadowing:ordinary and ergodic[J]. Journal of Mathematical Analysis and Applications, 2010, 364:151-155. doi: 10.1016/j.jmaa.2009.11.004
[11]	OPROCHA P, DASTJERDI D A, HOSSEINI M. On partial shadowing of complete pseudo-orbits[J]. Journal of Ma-thematical Analysis and Applications, 2013, 404:47-56. doi: 10.1016/j.jmaa.2013.02.068
[12]	冀占江.乘积空间与拓扑群作用下逆极限空间的动力学性质[D].南宁: 广西大学, 2014. JI Z J. Dynamical property of product space and the inverse limit space of a topological group action[D]. Nanning: Guangxi University, 2014.
[13]	AHMADI S A. Invariants of topological G-conjugacy on G-spaces[J]. Mathematica Moravica, 2014, 18(1):67-75. doi: 10.5937/MatMor1401067A
[14]	EKTA S, TARUN D. Consequences of shadowing property of G-spaces[J]. International Journal of Mathematical Analysis, 2013, 7(12):579-588. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=Doaj000002317151
[15]	RUCHI D, TARUN D. On properties of G-expansive homeomorphisms[J]. Mathematica Slovaca, 2012, 62(3):531-538. http://www.wanfangdata.com.cn/details/detail.do?_type=perio&id=10.2478/s12175-012-0028-7

Cited By

Cited by

Periodical cited type(4)

1.	冀占江. G-跟踪性和G-周期跟踪性研究. 浙江大学学报(理学版). 2023(04): 429-433 .
2.	冀占江，陈占和，张更容. 逆极限以及双重逆极限空间中利普希次跟踪性和几乎周期点的研究. 山西大学学报(自然科学版). 2022(02): 343-347 .
3.	冀占江，张更容. 强一致收敛下弱几乎周期点和周期序列跟踪性的研究. 华南师范大学学报(自然科学版). 2021(02): 110-113 .
4.	时伟，冀占江，覃桂茳，吴海龙. 群作用下移位映射的极限跟踪性. 数学的实践与认识. 2021(16): 196-199 .

Other cited types(0)

Get Citation

PDF

XML

Article views (1433) PDF downloads (43) Cited by(4)

Turn off MathJax

Article Contents

Abstract

References

The Strong G-shadowing Property of the Inverse Limit Spaces and the Product Spaces of Group Action

Abstract

References

Cited by

Periodical cited type(4)

Other cited types(0)

Catalog

Export File

Citation

Format

Content