An attempt to differential Galois theory of second order polynomial system and solvable subgroup of Mobius transformations

作者：Guan Ke ying^*; Lei Jin zhi

来源：Science in China Series A-Mathematics, 2007, 50(5): 748-760.

DOI：10.1007/s11425-007-2079-8

• conformal differential Galois group
• Mobius transformations
• integrability in the sense of Liouville

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 M6bius transformations at the first author's article published in this journal in 1996 are refreshed in this paper.

• 出版日期2007-5
• 单位清华大学; 北京交通大学