On the convergence of exotic formal series solutions of an ODE. A proof by the implicit mapping theorem

Renat Gontsov, Irina Goryuchkina

We propose a sufficient condition of the convergence of a complex power type formal series of the form $\phi ={\sum }_{k=1}^{\infty }{\alpha }_k(x^{\mathrm{i}\gamma })x^k$, where ${\alpha }_k$ are functions mero…