Title: A metric of mutual energy and unlikely intersections for dynamical systems,
Abstract: We introduce a metric of mutual energy for adelic measures associated to the
Arakelov-Zhang pairing. Using this metric and potential theoretic techniques
involving discrete approximations to energy integrals, we prove an effective
bound on a problem of Baker and DeMarco on unlikely intersections of dynamical
systems, specifically, for the set of complex parameters $c$ for which $z=0$
and $1$ are both preperiodic under iteration of $f_c(z)=z^2 + c$.