Global analysis of monodromy group of a riccati equation of torus T~2

摘要

For a particular Riccati equation on torus T~2 z'=z~2-λ (t), t∈T~2 an exact relation(28)between the generators of its monodromy group and the parameterλ∈R is obtained, so that the dependence of the properties of the monodromy group on the parameterλcan be discussed globally. It is proved that the limit set of the monodromy group has a fractal structure if and only if λ<-1/4.