In the hyperbolic case, the Julia-Lavaurs sets can be defined as
possible limits
of the Julia sets of the polynomials $z^2+c$ in the Hausdorff metric,
when the parameter $c$ tends to $1/4$. We will study continuity of the
Hausdorff dimension
of the Julia-Lavaurs sets on the boundary of the hyperbolic component
containing the real line.
The talk will follow the speaker's paper in Fund. Math. 214 (2011), no.
2, 119-133.