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Title:	On some chaos notions of dynamical systems
Authors:	Malouh Abdelmuhdi Ahmad Baloush (P83535)
Supervisor:	Syahida Che DzulKifli, Dr.
Keywords:	Chaotic Chaos notions Universiti Kebangsaan Malaysia -- Dissertations Dissertations, Academic -- Malaysia
Issue Date:	17-Jan-2019
Description:	In this work we focus on seven properties associated with chaotic behaviour; locally everywhere onto, topologically mixing, totally transitive, strong dense periodicity property, Devaney chaos, weakly blending and the specification property. Firstly, we look at these chaos notions on general compact spaces. We discuss the relations between these chaos notions, prove the positive relations and provide counterexamples for the negative relations. We summarize these finding by giving a hierarchy of these chaos notion to present their strength in terms of implication ability. In the subsequent chapter, we look at more specific space, shift spaces. We firstly consider all 1-step shift of finite type spaces and look at the chaotic behaviour of each space. It is concluded that on 1-step shift of finite type, the properties of locally everywhere onto, topologically mixing, totally transitive, the strong dense periodicity property, Devaney chaos, and the specification property are equivalent. By using higher block presentation, we propose that the relation may be true on all shift of finite type. Its turn out that, this is not the case for both shift of finite type and shift of infinite type. We summarize the finding on shift of finite type on a hierarchy of the seven chaos properties. We end up this chapter by distinguishing the chaos relations on finite and infinite type of shift space. Since one of the seven chaos concepts (i.e., the strong dense periodicity property) is a new well defined property, another aim of this project is to prove the significance of this concept in chaos study and propose a new chaos definition to improve comprehension study on the diversity of chaos definition. In the other aspects, we study the preservation of the chaos notions between two dynamical systems under conjugacy, semiconjugacy, quasiconjugacy, and 1-1 quasiconjugacy. In the last chapter, we investigate the dynamics of supra topological space and define some supra chaos notions, i.e., supra transitive, supra totally transitive, supra mixing, supra locally everywhere onto, and supra weakly blending in analogue to chaos notions of classical topological spaces. Supra open set is a generalization of various notions of open sets includes preopen sets, semiopen sets etc. which have been attracted a lot of attention in topological dynamics study. In supra topological dynamics, we prove some important results in classical topological dynamics. We also introduce and define the concept of supra conjugacy, and investigate the preservation of the above mentioned supra chaos characterizations under this supra conjugacy.,'Certification of Master's/Doctoral Thesis' is not available,Ph.D.
Pages:	170
Publisher:	UKM, Bangi
Appears in Collections:	Faculty of Science and Technology / Fakulti Sains dan Teknologi

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