| Summary: | 碩士 === 中原大學 === 數學系 === 87 === It is not too difficult to image that when n is sufficiently large,the behavior of orbits of the dynamical system ■in ■ can be very complicated.
The main purpose of this thesis is to inverstigate the behavior of orbits and the representation of orbits in terms of the graphs .
Note that every entry■ of the system's govenor , the matrix■ ,belongs to■ .■denotes the characteristic polynomial of■ and factoring■,■.Let■,■.Then it can be proved that■and also ,the behaviors of iteration of■in■and■can be represented as a tree and cycles respectively .The major contribution of this thesis is to present a simple algorithm for constructing the whole graph of the
iteration of the system by utilizing the graphs of iteration of the system in■ and■.
This thesis can be organized as follow.Section one and two contain all notations and definitions which are needed in the thesis .In section three ,we prove the main Theorem .In section four ,some examples are given for demonstraction .In the appendix ,we summarize n=3 case and classfy them into eight different patterms.
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