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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Automorphisms of compact Kähler manifolds with slow dynamics

Authors: Serge Cantat and Olga Paris-Romaskevich
Journal: Trans. Amer. Math. Soc. 374 (2021), 1351-1389
MSC (2020): Primary 14H37, 37A35
Published electronically: November 2, 2020
MathSciNet review: 4196396
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Abstract: We study automorphisms of compact Kähler manifolds having slow dynamics. Adapting Gromov’s classical argument, we give an upper bound on the polynomial entropy and study its possible values in dimensions $2$ and $3$. We prove that every automorphism with sublinear derivative growth is an isometry; a counter-example is given in the $C^{\infty }$ context, answering negatively a question of Artigue, Carrasco-Olivera, and Monteverde in [Acta Math. Hungar. 152 (2017), pp. 140–149] on polynomial entropy. We also study minimal automorphisms of surfaces with respect to the Zariski or euclidean topology.

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Additional Information

Serge Cantat
Affiliation: Univ Rennes, CNRS, IRMAR - UMR 6625, F-35000 Rennes, France
MR Author ID: 614455

Olga Paris-Romaskevich
Affiliation: Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France
MR Author ID: 1078211

Received by editor(s): February 16, 2020
Received by editor(s) in revised form: February 16, 2020, and June 24, 2020
Published electronically: November 2, 2020
Article copyright: © Copyright 2020 American Mathematical Society