An attempt to differential Galois theory of second order polynomial system and solvable subgroup of Mbius transformations |
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作者姓名: | Ke-ying GUAN & Jin-zhi LEI School of Science Beijing Jiaotong University Beijing China Zhou Pei-Yuan Center for Applied Mathematics Tsinghua University Beijing China |
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作者单位: | Ke-ying GUAN & Jin-zhi LEI School of Science,Beijing Jiaotong University,Beijing 100044,China; Zhou Pei-Yuan Center for Applied Mathematics,Tsinghua University,Beijing 100084,China |
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摘 要: | By introducing the conception "relativistic differential Galois group" for the second order polynomial systems, we establish the relation between the conformal relativistic differential Galois group and the subgroup of Mobius transformations, and prove that the system is integrable in the sense of Liouville if its conformal relativistic differential Galois group is solvable with a derived length at most 2. Some omissions on the structures of solvable subgroups of Mobius transformations at the first author's article published in this journal in 1996 are refreshed in this paper.
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