Dissertation
Dissertation > Mathematical sciences and chemical > Mathematics > Dynamical systems theory

On the Research of Some Problems in Topological Dynamical Systems

Author JinXiangHua
Tutor ChenErMing
School Huaqiao University
Course Basic mathematics
Keywords Power system Invariant set Delivery system Minimal system Equicontinuous system Replies point Chaos Enveloping semigroup Factor map Category Functor
CLC O19
Type Master's thesis
Year 2011
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A characterization of a class of dynamical systems in a collection of L ( x 1 < / sub > x 2 ) were made to promote the study nature and obtained degrees continuous system . Also use the concept of scope and category theory functor in depth discussion on the relationship between the power system and its enveloping semigroup . In the first chapter introduces the necessary definitions and notations . Described in [ 4 ] and [ 5 ] In the second chapter , a collection of classes L (x 1 , x 2 ) was further discussed . First , its definition made ??the promotion , and research related to the nature of the collection class promotion , and then given a characterization of the equicontinuous system . Second, the collection L ( x 1 < / sub > , x 2 < / sub > ) , L (x 1 , x 2 < / sub > , x 3 ), L (x 1 , x 2 , x 3 , x 4 ) , ... , L ( x 1 < / sub > , ... , X n < / sub > ) , the relationship between the discussion, and to give some examples . In the third chapter , the concept of the use of category theory in the category and functor , define the areas of power system the envelope the semigroup areas E the covariant functor F 1 as well as areas T to T to the scope of E * anti- change functor F 2 . In addition , and also discuss the package of the product of the system in the areas of T enveloping semigroup and category E enveloping semigroup direct product consistency and the areas T in inverse limit system the enveloping semigroup areas E network semigroup inverse limit consistency .

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