%0 Report %D 2013 %T Equilibrium measures for a class of potentials with discrete rotational symmetries %A Ferenc Balogh %A Dario Merzi %X In this note the logarithmic energy problem with external potential $|z|^{2n}+tz^d+\bar{t}\bar{z}^d$ is considered in the complex plane, where $n$ and $d$ are positive integers satisfying $d\leq 2n$. Exploiting the discrete rotational invariance of the potential, a simple symmetry reduction procedure is used to calculate the equilibrium measure for all admissible values of $n,d$ and $t$. It is shown that, for fixed $n$ and $d$, there is a critical value $|t|=t_{cr}$ such that the support of the equilibrium measure is simply connected for $|t|t_{cr}$. %I SISSA %G en %U http://hdl.handle.net/1963/7230 %1 7270 %2 Mathematics %4 1 %$ Submitted by Dario Merzi (dmerzi@sissa.it) on 2013-12-09T12:34:49Z No. of bitstreams: 1 1312.1483v1.pdf: 784215 bytes, checksum: 156588817c77f32a8a48f1a5a0b480ca (MD5)