Eventual Fitting Shadowing Property for Hyperbolic Dynamical Systems
DOI:
https://doi.org/10.29304/jqcm.2023.15.3.1281Keywords:
Hyperbolic sets, Pseudo-orbits, Eventual fitting shadowing, Residual sets, Chain transitive.Abstract
Let be a diffeomorphism map on a closed smooth manifold for dimension . We explain in this work any chain transitive set of generic diffeomorphism , if a diffeomorphism has another type of shadowing property is called, the eventual shadowing property on locally maximal chain transitive set, then is hyperbolic. In general, the eventual fitting shadowing property is not fulfilled in hyperbolic dynamical systems (satisfy in case L is Anosov diffeomorphism map) . In this paper, several concepts were presented. These concepts can be re-examined on other important spaces, and their impact on finding dynamical characteristics that may be employed in solving some mathematical problems.
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References
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[10] M. Lee," Vector Fields satisfying the barycenter property," Open Math., vol.16, no. 1, (2018),pp. 429-436.
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[12] D. Meihua ,W. Jung and C. Morales," Eventually shadowable points ,"Qualitative Theory of Dynamical Systems,vol.19, no. 1,(2020),pp. 1-11.
[13] C. Sylvain,"Periodic orbits and chain-transitive sets of C^1-diffeomorphisms," Publications Mathematiques de l'Institut des Hautes Études Scientifiques, vol. 104, no. 1, (2006),pp.87-141.
[14] A. Arbieto,"Periodic Orbits and Expansiveness," Math. Z., vol.269, no.3-4, (2011),pp.801-807.
[15] K. Sakai, "C^1-stably shadowable chain components," Ergodic Theory & Dynam. Syst., vol.28, (2008),pp. 987-1029.
[16] J. Franks," Necessary condition for stability of diffeomorphisms," Trans. Amer. Math. Soc., vol.158, (1971),pp.301-308.
[17] M. Lee and S. Lee, "Generic diffeomorphisms with robustly transitive sets," Common. Korean Math. Soc., vol.28, no. 3, (2013),pp.581-587.
[18] K. Lee and X. Wen, "Shadowable Chain Transitive Sets of C^1-generic diffeomorphisms," Bull. Korean Math. Soc., vol.49, no. 2, (2012),pp. 263-270.
[19] F. Abdenur , C. Bonatti and S. Crovisier ," Global dominated splittings and the C^1Newhouse phenomenon,"Proc. Amer. Math. Soc., vol.134,no.8, (2006),pp. 2229-2237.
[2] F.W. Kamel and I.M.T. AL-Shara'a, "Some Chaotic Results of Product on Zero Dimension Spaces," Iraqi Journal of Science, vol.61,no.2, (2020),pp. 428-434.
[3] R.S.A. AL-Juboory and I.M.T. AL-Shara'a, "Some Chaotic Properties of G- Average Shadowing Property," Iraqi Journal of Science, vol.61, no.7, (2020),pp. 1715-1723.
[4] Y.J. Ajeel and S.N. Kadhim," Some Common Fixed Points Theorems of Four Weakly Compatible Mappings in Metric Spaces," Baghdad Journal of Science, vol.18, no. 3, (2021),pp. 543-546.
[5] H. Hadeel and A .Salwa," Fixed Point Theorems in General Metric Space with an Application," Baghdad Journal of Science, vol.18, no.1, (2021),pp.812-815.
[6] M. Lee, "Orbital Shadowing Property on Chain Transitive Sets for Generic Diffeomorphisms," Act Univ. Sapientiae Math., vol.12, no.1, (2020),pp. 146-154.
[7] M. Lee,"Asymptotic orbital shadowing property for diffeomorphisms,"Open Mathematics, vol.17, no. 1, (2019),pp. 191-201 .
[8] M. Lee and J. Park ,"Vector Fields with the Asymptotic Orbital Pseudo-orbit Tracing Property," Qualitative theory of dynamical systems,vol.19, no. 2, (2020),pp.1-16.
[9] Lee M. ,"A type of The Shadowing Property for Generic View Points," Axioms, vol.7, no. 1, (2018),pp. 18.
[10] M. Lee," Vector Fields satisfying the barycenter property," Open Math., vol.16, no. 1, (2018),pp. 429-436.
[11] M. Lee," Eventual Shadowing for Chain Transitive Sets of C^1 Generic Dynamical Systems," Korean Math. Soc. J., vol.58, no.5, (2021),pp. 1059-1079.
[12] D. Meihua ,W. Jung and C. Morales," Eventually shadowable points ,"Qualitative Theory of Dynamical Systems,vol.19, no. 1,(2020),pp. 1-11.
[13] C. Sylvain,"Periodic orbits and chain-transitive sets of C^1-diffeomorphisms," Publications Mathematiques de l'Institut des Hautes Études Scientifiques, vol. 104, no. 1, (2006),pp.87-141.
[14] A. Arbieto,"Periodic Orbits and Expansiveness," Math. Z., vol.269, no.3-4, (2011),pp.801-807.
[15] K. Sakai, "C^1-stably shadowable chain components," Ergodic Theory & Dynam. Syst., vol.28, (2008),pp. 987-1029.
[16] J. Franks," Necessary condition for stability of diffeomorphisms," Trans. Amer. Math. Soc., vol.158, (1971),pp.301-308.
[17] M. Lee and S. Lee, "Generic diffeomorphisms with robustly transitive sets," Common. Korean Math. Soc., vol.28, no. 3, (2013),pp.581-587.
[18] K. Lee and X. Wen, "Shadowable Chain Transitive Sets of C^1-generic diffeomorphisms," Bull. Korean Math. Soc., vol.49, no. 2, (2012),pp. 263-270.
[19] F. Abdenur , C. Bonatti and S. Crovisier ," Global dominated splittings and the C^1Newhouse phenomenon,"Proc. Amer. Math. Soc., vol.134,no.8, (2006),pp. 2229-2237.
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Published
2023-09-30
How to Cite
AL-Ftlawy, D. M., & AL-Shara, I. M. (2023). Eventual Fitting Shadowing Property for Hyperbolic Dynamical Systems. Journal of Al-Qadisiyah for Computer Science and Mathematics, 15(3), Math Page 41–53. https://doi.org/10.29304/jqcm.2023.15.3.1281
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Math Articles
