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arXiv · 2502.20103

Equidistribution of saddle periodic points for H\'enon-like maps

Muhan Luo·Qi Zhou
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Abstract

We prove that under the natural assumption over the dynamical degrees, the saddle periodic points of a H\'enon-like map in any dimension equidistribute with respect to the equilibrium measure. Our work is a generalization of results of Bedford-Lyubich-Smillie, Dujardin and Dinh-Sibony along with improvements of their techniques. We also investigate some fine properties of Green currents associated with the map. On the pluripotential-theory side, in our non-compact setting, the wedge product of two positive closed currents of complementary bi-degrees can be defined using super-potentials and the density theory. We prove that these two definitions are coherent.

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Muhan Luo, Qi Zhou. 2025-02-27. Equidistribution of saddle periodic points for H\'enon-like maps. https://arxiv.org/abs/2502.20103

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