TY - RPRT
T1 - Equilibrium measures for a class of potentials with discrete rotational symmetries
Y1 - 2013
A1 - Ferenc Balogh
A1 - Dario Merzi
AB - 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 $|t|t_{cr}$.
PB - SISSA
UR - http://hdl.handle.net/1963/7230
N1 - 23 pages, 3 figures
U1 - 7270
U2 - Mathematics
U4 - 1
ER -