01024nas a2200121   4500008004100000245008800041210006900129260001000198520062200208100001900830700001700849856003600866       2013                        en  d00aEquilibrium measures for a class of potentials with discrete rotational  symmetries0 aEquilibrium measures for a class of potentials with discrete rot  bSISSA3 aIn 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 $|t|<t_{cr}$ and has $d$ connected components for $|t|>t_{cr}$.1 aBalogh, Ferenc1 aMerzi, Dario  uhttp://hdl.handle.net/1963/7230