We consider a resolution of ramified irregular singularities of meromorphic<br />
connections on a formal disk via local Fourier transforms. A necessary and<br />
sufficient condition for an irreducible connection to have a resolution of the<br />
ramified singularity is determined as an analogy of the blowing up of plane<br />
curve singularities. We also relate the irregularity of Komatsu and Malgrange<br />
of connections to the intersection numbers and the Milnor numbers of plane<br />
curve germs. Finally, we shall define an analogue of Puiseux characteristics<br />
for connections and find an invariant of the family of connections with the<br />
fixed Puiseux characteristic by means of the structure of iterated torus knots<br />
of the plane curve germs.