Open Access
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On Attractor and Pseudo Orbit Tracing of Uniform Limit Dynamical Systems
*Phinao RamwungzanCorresponding authorazanphinao@gmail.comDepartment of Mathematics, Manipur University-Canchipur, Imphal, Manipur, 795003, IndiaView full profile → , Khundrakpam Binod Mangangkhubim@manipuruniv.ac.inDepartment of Mathematics, Manipur University-Department Of Mathematics, Manipur University-Canchipur, Imphal, Manipur, 795003, ManipurView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 22 May 2018
- Accepted:
- 27 Aug 2018
- Published Online:
- 02 Jan 2019
- Article type:
- Article
- Language:
- EN
- Article no.:
- 1726037X.2018.1551719
- Pages:
- 83–90
Abstract
Some dynamical properties of the uniform limit dynamical system have been investigated. It has been found that for a sequences undefined of dynamical systems having same attractor undefined and converging uniformly to a dynamical system undefined the dynamical system undefined has the same attractor undefinedIt has been found that a sequence undefined of uniformly rigid dynamical systems converging uniformly to a dynamical system undefined the dynamical system undefined is also uniformly rigid. We have proved that the uniform limit undefined of a uniformly convergent sequence of dynamical systems having pseudo orbit tracing property has pseudo orbit tracing property. The expansiveness and the equicontinuous set ϵ: of the uniform limit dynamical system have been investigated.
Keywords
Subject Classifications
37B2037B5554H20
References
L.S.Block and W.A.Coppel, Dynamics in one dimension, Springer Verlag , 1992 . M.Brin and GarrettStuck, Introduction to dynamical systems, Cambridge University Press , 2002 . M.Denker, C.Grillenberger and K.Sigmund, Ergodic theory on compact spaces, Lecture Notes in Math ., , Springer , ( 1977 ). R.Devaney, An introduction to chaotic dynamical systems, 2nd ed. , Westview , 2003 . J.Dvorakova, Chaos in non-autonomous discrete dynamical systems, Communications in Non-linear Svience and Numerical aimulation , ( 2012 ), 4649 - 4652 . A.Fedeli and A.L.Donne, A note on the uniform limit of transitive dynamical systems, Bull, Belg. Math. Soc.Simen Stevin , ( 2009 ), 59 - 66 . R.F.Heriberto, Uniform convergence and transitivity. S.Kolyada and L.Snoha, Some aspects of topololgical transitivity-a survey, Grazer. Math. Ber ., , 3 ( 1997 ). P.Kurka, Topological and symbolic dynamics. K.B.Mangang, Equicontinuity of the limit function of a sequence of equicontinuous functions, Journal of Indian Math. Soc ., ( 1-2 )( 2014 ), 115 - 121 . K.BMangang, Topological mixing of the limit function of a sequence of dynamical systems, Bull, Cal. Math. Soc. , ( 1 )( 2017 ), 45 - 54 . A.S.Raghib, A.S and A.H.Kifah, Uniform convergence and chaotic behaviour, Nonlinear Analysis , ( 2006 ), 993 . A.S.Raghib, M.G.Felix and P.Alfredo, Erratum to uniform convergence and chaotic be- haviour. D.Ruchi and D.Tarun, Topological transitivity of uniform limit functions on G-spaces, Int. Journal Math. Analysis , ( 2012 ), 1491 - 1499 . A.N.Sharkovsky, Nonwandering points and the centre of a continuous mapping of the line in itself, Dopovidi Ukrain. Acad. Sci ., ( 1964 ), 865 .(in Ukrainian) C.Tian and G.Chen, Chaos of sequence of maps in a metric space, Chaos, Solitons and Fractals , ( 2006 ), 1067 - 1075 . M.Vellokoop and R.Berlund, On interval, transitivity = Chaos, Amer. Math. Monthly , ( 1994 ), 353 . K.Yang, F.Zeng and G.Zhang, Devaney’s chaos on uniform limit maps, Fractals , ( 2011 ), 522 - 525 .
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