Orbit counting in polarized dynamical systems

Abstract

<p style='text-indent:20px;'>We extend recent orbit counts for finitely generated semigroups acting on <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{P}^N $\end{document}</tex-math></inline-formula> to certain infinitely generated, polarized semigroups acting on projective varieties. We then apply these results to semigroup orbits generated by some infinite sets of unicritical polynomials.</p>