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Equidistribution of saddle periodic points for Hénon-type automorphisms of \(\mathbb {C}^k\)

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Abstract

In this paper, we prove the equidistribution of saddle periodic points for Hénon-type automorphisms of \(\mathbb {C}^k\) with respect to its equilibrium measure. A general strategy to obtain equidistribution properties in any dimension is presented. It is based on our recent theory of densities for positive closed currents. Several fine properties of dynamical currents are also proved.

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Notes

  1. Throughout the paper, the positivity of (p, p)-currents is in the strong sense.

  2. The terminology is changed with respect to the one in [7].

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Acknowledgments

The paper was partially written during the visit of the first author at the Shanghai Center for Mathematical Sciences. He would like to thank the institute, Yi-Jun Yao and Weiping Zhang for their great hospitality.

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Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, 10 Lower Kent Ridge Road, Singapore, 119076, Singapore

    Tien-Cuong Dinh

  2. Université Paris-Sud, Mathématique-Bâtiment 425, 91405, Orsay, France

    Nessim Sibony

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  1. Tien-Cuong Dinh
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  2. Nessim Sibony
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Correspondence to Tien-Cuong Dinh.

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Dinh, TC., Sibony, N. Equidistribution of saddle periodic points for Hénon-type automorphisms of \(\mathbb {C}^k\) . Math. Ann. 366, 1207–1251 (2016). https://doi.org/10.1007/s00208-016-1369-2

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