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Equidistribution of saddle periodic points for H\'enon-like maps
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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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Continuous local potential functionals and the Dinh-Sibony product
On any complex manifold, the Dinh-Sibony product of three positive closed currents is well defined and associative when the first current has continuous local potential functionals and the other two satisfy Condition (I).
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