  Let $f$ be a germ of holomorphic diffeomorphism with an irrationally
indifferent fixed point at the origin in $\mathbb{C}$ (i.e. $f(0) = 0, f'(0) =
e^{2\pi i \alpha}, \alpha \in \mathbb{R} - \mathbb{Q}$). Perez-Marco showed the
existence of a unique continuous monotone one-parameter family of nontrivial
invariant full continua containing the fixed point called Siegel compacta, and
gave a correspondence between germs and families $(g_t)$ of circle maps
obtained by conformally mapping the complement of these compacts to the
complement of the unit disk. The family of circle maps $(g_t)$ is the orbit of
a locally-defined semigroup $(\Phi_t)$ on the space of analytic circle maps
which we show has a well-defined infinitesimal generator $X$. The explicit form
of $X$ is obtained by using the Loewner equation associated to the family of
hulls $(K_t)$. We show that the Loewner measures $(\mu_t)$ driving the equation
are 2-conformal measures on the circle for the circle maps $(z \mapsto
\overline{g_t(\overline{z})})$.
