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Research in Integrability of Several Classes of Autonomous Systems Based on Lie Group Theory

Author: LiFangFang
Tutor: HuYanXia
School: North China Electric Power University (Beijing)
Course: Applied Mathematics
Keywords: Lee (Lie) group Integrability Integrating factor First integral The necessary and sufficient conditions
CLC: O152.5
Type: Master's thesis
Year: 2010
Downloads: 37
Quote: 0
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Abstract


Lee (Lie) group theory integrability of the second, third , and n-order autonomous system . The main content and results , including the following aspects : (1) First , given the appropriate second-order autonomous system to accept the single- parameter Lie group of the general form of the generator , and then discuss some properties of the system ; given two types of special form of second-order autonomous system to accept the single- parameter Lie group of the general form of the generator , and an integrating factor of the system is constructed . ( 2 ) is based on the theory of Lie groups , order autonomous system acceptable to the two single- parameter Lie generator of seeking the methods and conclusions of the integrating factor of the system is presented and proved . (3) For the n-order autonomous system , when the system is conservative system , discussed the integral factor and the first integral relationship ; system for non- conservative system is given and proved the necessary and sufficient condition for the existence of the system integrating factor .

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CLC: > Mathematical sciences and chemical > Mathematics > Algebra,number theory, portfolio theory > Group theory > Lie group
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