  Let $f(z) = e^{2\pi i \alpha}z + O(z^2), \alpha \in \mathbb{R}$ be a germ of
holomorphic diffeomorphism in $\mathbb{C}$. For $\alpha$ rational and $f$ of
infinite order, the space of conformal conjugacy classes of germs topologically
conjugate to $f$ is parametrized by the Ecalle-Voronin invariants (and in
particular is infinite-dimensional). When $\alpha$ is irrational and $f$ is
nonlinearizable it is not known whether $f$ admits quasi-conformal
deformations. We show that if $f$ has a sequence of repelling periodic orbits
converging to the fixed point then $f$ embeds into an infinite-dimensional
family of quasi-conformally conjugate germs no two of which are conformally
conjugate.
