The Möbius transform effect in singular systems of differential equations

作者：

Highlights：

• M-systems appear after applying the Möbius transform to the pencil of a system of differential equations.

• We provide a link between the solutions of a singular linear system and the solutions of its corresponding M-systems.

• By using the invariants of the initial system we obtain information (existence, uniqueness of solutions) for the M-systems.

• This enables us to construct explicit solutions of each M-system, without resorting to further processes of computation.

摘要

•M-systems appear after applying the Möbius transform to the pencil of a system of differential equations.•We provide a link between the solutions of a singular linear system and the solutions of its corresponding M-systems.•By using the invariants of the initial system we obtain information (existence, uniqueness of solutions) for the M-systems.•This enables us to construct explicit solutions of each M-system, without resorting to further processes of computation.

论文关键词：Singularity,Dynamical system,Möbius transform,Initial conditions,Differential equations

论文评审过程：Received 21 December 2018, Revised 20 May 2019, Accepted 27 May 2019, Available online 8 June 2019, Version of Record 8 June 2019.

论文官网地址：https://doi.org/10.1016/j.amc.2019.05.047