ISSN 2394-5125
 

Review Article 


Some Chaotic Properties of G- periodic Shadowing Property

Raad Safah Abood AL – Juboory, Iftichar M. T. AL - Shara’a.

Abstract
Let (M,É— ) be a metric G-space and ɸ ∶M→M be a continuous map. This paper aims to study the idea of the G-periodic shadowing property (G Per.SP ) for a continuous map on G-space and achieves the relative of the G Per.SP with G-shadowing property (G SP). Also, if ɸ has the G Per.SP, then ɸ^n has the G Per.SP for every n∈N. We show that if ɸ is a G –expansive and has the G SP then ɸ has the G Per.SP, and if the map ɸ on compact metric G-space has G-chain transitive and the G Per.SP, then ɸ has the G SP with G-transitivity. We show that the map ɸ on compact metric G-space, ɸ is a G–expansive and G-chain mixing, if ɸ^n has G Per.SP for some n∈N,such that n≠1 then ɸ has G Per.SP. Moreover, we prove that if a map ɸ be pseudo-equivariant with dense set of G_ɸ-periodic points which has the G Per.SP and G-average shadowing property(GASP) then ɸ is G-chain mixing. Finally, we show that if (M,É— ) is a compact metric G-space having two points at least, ɸ be a G-distal homeomorphism and ɸ is G-chain mixing , then ɸ does not have the G Per.SP.

Key words: G-shadowing; periodic shadowing; G-periodic shadowing; G –expansive; The G-average shadowing; G-transitivity ; topologically G-chain mixing.


 
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Pubmed Style

Raad Safah Abood AL - Juboory, Iftichar M. T. AL - Shara'a. Some Chaotic Properties of G- periodic Shadowing Property. JCR. 2020; 7(1): 167-170. doi:10.22159/jcr.07.01.29


Web Style

Raad Safah Abood AL - Juboory, Iftichar M. T. AL - Shara'a. Some Chaotic Properties of G- periodic Shadowing Property. http://www.jcreview.com/?mno=302645221 [Access: February 21, 2020]. doi:10.22159/jcr.07.01.29


AMA (American Medical Association) Style

Raad Safah Abood AL - Juboory, Iftichar M. T. AL - Shara'a. Some Chaotic Properties of G- periodic Shadowing Property. JCR. 2020; 7(1): 167-170. doi:10.22159/jcr.07.01.29



Vancouver/ICMJE Style

Raad Safah Abood AL - Juboory, Iftichar M. T. AL - Shara'a. Some Chaotic Properties of G- periodic Shadowing Property. JCR. (2020), [cited February 21, 2020]; 7(1): 167-170. doi:10.22159/jcr.07.01.29



Harvard Style

Raad Safah Abood AL - Juboory, Iftichar M. T. AL - Shara'a (2020) Some Chaotic Properties of G- periodic Shadowing Property. JCR, 7 (1), 167-170. doi:10.22159/jcr.07.01.29



Turabian Style

Raad Safah Abood AL - Juboory, Iftichar M. T. AL - Shara'a. 2020. Some Chaotic Properties of G- periodic Shadowing Property. Journal of Critical Reviews, 7 (1), 167-170. doi:10.22159/jcr.07.01.29



Chicago Style

Raad Safah Abood AL - Juboory, Iftichar M. T. AL - Shara'a. "Some Chaotic Properties of G- periodic Shadowing Property." Journal of Critical Reviews 7 (2020), 167-170. doi:10.22159/jcr.07.01.29



MLA (The Modern Language Association) Style

Raad Safah Abood AL - Juboory, Iftichar M. T. AL - Shara'a. "Some Chaotic Properties of G- periodic Shadowing Property." Journal of Critical Reviews 7.1 (2020), 167-170. Print. doi:10.22159/jcr.07.01.29



APA (American Psychological Association) Style

Raad Safah Abood AL - Juboory, Iftichar M. T. AL - Shara'a (2020) Some Chaotic Properties of G- periodic Shadowing Property. Journal of Critical Reviews, 7 (1), 167-170. doi:10.22159/jcr.07.01.29





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