A metric of mutual energy and unlikely intersections for dynamical systems

Paul Fili

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arXiv · 1708.08403

A metric of mutual energy and unlikely intersections for dynamical systems

Paul Fili

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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 $f_c(z)=z^2 + c$.

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Paul Fili. 2017-08-28. A metric of mutual energy and unlikely intersections for dynamical systems. https://arxiv.org/abs/1708.08403

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