Hausdorff dimension of Julia sets (Q817117)

The paper is a nicely written brief survey on the fractal thermodynamic formalism for degenerations of Julia sets of complex quadratic polynomials. It highlights some of the results derived along with the following important result of \textit{M. Shishikura} [Ann. Math. (2) 147, 225--267 (1998; Zbl 0922.58047)]; see also the author [C. R. Acad. Sci., Paris, Sér. I, Math. 326, 1227--1232 (1998; Zbl 0924.30035)]; \textit{S.-M. Heinemann} and \textit{B. O. Stratmann} [Math. Z. 237, 571--583 (2001; Zbl 0991.37031)]. With \(d(\mu)\) referring to the Hausdorff dimension of the Julia set of the map \(z \mapsto z^2+ \mu z\), we have for \(\lambda=\exp(2 \pi i m/n) (m,n \in {\mathbb N}, gcd(m,n)=1), \) \( \liminf_{\mu \to \lambda {\text{ tangential}}} d(\mu) > \frac{2n}{n+1}.\)