%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
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