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Vol3 Issue2 _3

posted Mar 23, 2019, 11:40 PM by Yaseen Raouf Mohammed   [ updated Apr 7, 2019, 5:45 AM ]
 TRANSITIVE MAPS ON DIFFERENTIAL MANIFOLDS

 Mohammed Nokhas Murad Kaki

 Mathematics Department, College of Science, University of Sulaimani.

 Yue Fang Loh

 Department of Actuarial Science and Applied Statistics, Faculty of Business and Information Science, UCSI University, Kuala Lumpur, Malaysia.


 Abstract.
In this paper, the author has defined a new class of transitive sets and mixing sets called D-transitive sets and called D-mixing sets respectively and he has proved that every weakly D-mixing subset in a differential manifold M implies D-transitive subset of M but not conversely, and that these new definitions are all preserved under Dconjugation. Finally, we illustrate by theorems the relevant topologically D-transitive and D-chaotic behavior by some maps defined on a differential manifold and relationship between the new and basic definitions of transitive sets are given.


 Keywords: 
D-transitive sets, weakly D-mixing chaos, D-Conjugation and topological manifold.


 REFERENCES
[1] Antoni A. Kosinski, [1993], Differential manifolds, Volume 138 in Pure and Applied Mathematics.
[2] Mohammed N. Murad, [2014], New types of chaos and non-wandering points in topological spaces, Pure and Applied Mathematics Journal, SciencePG.
[3] A.W. Brown, [2010], Nonexpanding Attractors: Conjugacy to Algebraic Models and Classification in 3-Manifolds, J. Mod. Dyn. V. 4, No. 3, 517548.
[4] A. Flavio, & C. Sylvain, [2011], Transitivity and topological mixing for C1 diffeomorphisms. Essays in Mathematics and its Applications: In Honor of Stephen Smale’s 80th Birthday.
[5] https://en.wikipedia.org/wiki/Generic_property

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