We consider the chordal L\"owner differential equation with the model driving function $\root3\of t$. Holomorphic and singular solutions are represented by their series. It is shown that a disposition of values of different singular and branching solutions is monotonic, and solutions to the L\"owner equation map slit domains onto the upper half-plane. The slit is a $C^1$-curve. We give an asymptotic estimate for the ratio of harmonic measures of the two slit sides.
Categories: math.CV