On convergence sets of divergent power series

Abstract

A nonlinear generalization of convergence sets of formal power series, in the sense of Abhyankar–Moh [J. Reine Angew. Math. 241 (1970)], is introduced. Given a family $ y=\varphi _{s}(t,x)=sb_{1}(x)t+b_{2}(x)t^{2}+\cdots$ of analytic curves in $% \