Several generalized K-shadowing properties characteristics in metric space


Abstract views: 133 / PDF downloads: 86

Authors

  • Anwer Ahmed Saleh University of Sfax, Departement of Mathematiques, Tunisia
  • Mohamed Hbaib University of Sfax, Departement of Mathematiques, Tunisia

Keywords:

Shadowing, K-shadowing, Metric space

Abstract

We focus here on K-shadowing characteristic due to its significant mathematical aspects and application. Several of the format’s common characteristics are demonstrated in this essay. If (W, d) is a metric space with dimensions z,v : (W,d)→(W,d) be mapping have the K-shadowing characteristic. We demonstrate the K-shadowing properties of the mappings z ×v z + v , zn and zov.

References

Bowen, R., Equilibrium states and the ergodic theory of Anosov diffeomorphisms. Springer Lecture Notes in Math, 470, (1975), 78–104.

Han, Y., and Lee, K., Inverse shadowing for structurally stable flows. Dynamical Systems, 19 (4), (2004), 371–388.

Bowen, R. E., Equilibrium states and the ergodic theory of Anosov diffeomorphisms (Vol. 470). Springer Science & Business Media, (2008).

Bowen, R., Ergodic theory of axiom a diffeomorphism. Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, (2006), 90–107.

Bowen, R. E., Chazottes, J. R., Ruelle, D., Bowen, R. E., Chazottes, J. R., and Ruelle, D., Ergodic theory of axiom a diffeomorphism. Equilibrium States and the Ergodic Theory of Anosov Diffeomorphisms, (2008), 61–73.

Walters, P., On the pseudo orbit tracing property and its relationship to stability. The Structure of Attractors in Dynamical Systems: Proceedings, North Dakota State University, June 20–24, 1977, (2006), 231–244.

Yang, R. S., and Shen, S. L., Pseudo-orbit-tracing and completely positive entropy. Acta Mathematica Sinica, Chinese Series, 42 (1), (1999), 99–104.

Aoki, N., and Hiraide, K., Topological theory of dynamical systems: recent advances. (1994).

Blank, M. L. V., Small perturbations of chaotic dynamical systems. Russian Mathematical Surveys, 44 (6), (1989), 1.

Gilmore, R., Topological analysis of chaotic dynamical systems. Reviews of Modern Physics, 70 (4), (1998), 1455.

Zhang, G., Liu, Z., and Ma, Z., Generalized synchronization of different dimensional chaotic dynamical systems. Chaos, Solitons & Fractals, 32 (2), (2007), 773–779.

Dadras, S., Momeni, H. R., and Majd, V. J., Sliding mode control for uncertain new chaotic dynamical system. Chaos, Solitons & Fractals, 41 (4), (2009), 1857–1862.

Lucarini, V., Faranda, D., Wouters, J., and Kuna, T., Towards a general theory of extremes for observables of chaotic dynamical systems. Journal of statistical physics, 154, (2014), 723–750.

Ouannas, A., and Odibat, Z., Generalized synchronization of different dimensional chaotic dynamical systems in discrete time. Nonlinear Dynamics, 81, (2015), 765–771.

Kloeden, P., Ombach, J., and Pokrovskii, A., Continuous and inverse shadowing. J. Funct. Differ. Equ., 6, (1999), 135–151.

Pilyugin, S. Y., Shadowing in dynamical systems. Springer, (2006).

Diamond, P., Kloeden, P., Kozyakin, V., and Pokrovskii, A., Semi-Hyperbolicity and Bi-Shadowing. American Institute of Mathematical Sciences, (2012).

Diamond, P., Kloeden, P., Kozyakin, V., and Pokrovskii, A., Computer robustness of semi-hyperbolic mappings. Random and computational Dynamics, 3 (1), (1995), 57–70.

Anosov, D. V., Ergodic properties of geodesic flows on closed Riemannian manifolds of negative curvature. In Hamiltonian Dynamical Systems (pp. 486–489). CRC Press, (2020).

Al-Badarneh, A., Bi-shadowing of Contractive Set-Valued Mappings with Application to IFS’s: The Non-Convex Case. JJMS, 7 (4), (2014), 287–301.

Good, C., Mitchell, J., and Thomas, J., On inverse shadowing. Dynamical Systems, 35 (3), (2020), 539–547.

Al-Badarneh, A., and Karalc, J., Bi-shadowing of some classes of single-valued almost contractions. Applied Mathematical Sciences, 9 (58), (2015), 2859–2869.

Ajam, M. H., and Al-Shara’a, I. M., Types of Expansivity on Bi-Shadowing Property. In IOP Conference Series: Materials Science and Engineering (Vol. 928, No. 4, p. 042039). IOP Publishing, (2020, November).

Downloads

Published

2023-07-18

How to Cite

Anwer Ahmed Saleh, & Mohamed Hbaib. (2023). Several generalized K-shadowing properties characteristics in metric space. Results in Nonlinear Analysis, 6(2), 108–113. Retrieved from https://nonlinear-analysis.com/index.php/pub/article/view/226