  To explore the relation between properties of Loewner chains and properties
of their driving functions, we study Loewner chains driven by functions $U$ of
finite total variation. Under some appropriate conditions, we show existence of
the simple trace $\gamma$ and establish continuity of the map $U$ to $\gamma$
with respect to uniform topology on $\gamma$ and the total variation topology
on $U$. In the spirit of work of Wong and Tran-Lind, we also obtain conditions
on the driving function that ensures the trace to be continuously
differentiable.
