Inverse shadowing characteristic in Z-group

Zghair, Hayder Kadhim; Abood, Raad Safah; Al-Yaseen, May A. A.; Hadi, Mustafa Hasan

doi:10.47974/JDMSC-1929

Open Access Research Article

Inverse shadowing characteristic in Z-group

^*Hayder Kadhim ZghairCorresponding authorhyderkkk@uobabylon.edu.iqDepartment of Software College of Information Technology University of Babylon Department of Software College of Information Technology University of BabylonBabylon, 51001, IraqView full profile → , Raad Safah Aboodraadalhulali@gmail.comDirectorate of Education of Babylon Ministry of Education Directorate of Education of Babylon Ministry of EducationBabylon, 51001, IraqView full profile → , May A. A. Al-Yaseenpure.may.alaa@uobabylon.edu.iqDepartment of Mathematics College of Education for Pure Science University of Babylon Department of Mathematics College of Education for Pure Sciences University of BabylonBabylon, 51001, IraqView full profile → , Mustafa Hasan Hadipure.mustafa.hassan@uobabylon.edu.iqDepartment of Mathematics College of Education for Pure Science University of BabylonBabylon, 51001, IraqView full profile →

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pp. 1473–1478Vol. 27Issue 5August 2024DOI: 10.47974/JDMSC-1929 Crossmark XML

Received:: 07 Nov 2023
Published Online:: 26 Aug 2024
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1929
Pages:: 1473–1478

Abstract

In the realm of dynamical systems theory, shadowing plays a crucial role. Structurally stable diffeomorphisms exhibit a noteworthy characteristic known as the inverse shadowing characteristic, which is investigated within the context of continuous methods. On compact manifolds, hyperbolic homeomorphisms are demonstrated to possess both inverse shadowing and bi-shadowing characteristics, particularly concerning a class of δ methods. These methods are described as continuous mappings from the manifold into the space of bi-infinite sequences within the manifold, utilizing the product topology. Additionally, the shadowing characteristic of the Lipschitz inverse is explored concerning two distinct classes of approaches, which produce pseudo-trajectories for dynamical systems. In our research, we establish that the characteristic of inverse shadowing can be derived from several fundamental dynamical system characteristics, including structural stability, transversality, Anosov characteristics, expansivity, continuum-wise expansiveness, and expansion.

Keywords

Inverse shadowing Expansive Structurally stable

Subject Classifications

34D20

References

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