In this work we describe dicritical foliations in $(\mathbb{ C}^2,0)$ at a triple point of the resolution dual graph of an analytic plane branch $\mathcal{ C}$ using its semiroots. In particular, we obtain a constructive method to present a one-parameter family $\mathcal{ C}_{ u}$ of separatrices for such foliations. As a by-product we relate the contact order between a special member of $\mathcal{ C}_{ u}$ and $\mathcal{ C}$ with analytic discrete invariants of plane branches.
Categories: math.AG