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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.
MSC (2020): Primary 14H37, 37A35
DOI: https://doi.org/10.1090/tran/8229
Published electronically: November 2, 2020
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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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Serge Cantat
Affiliation: Univ Rennes, CNRS, IRMAR - UMR 6625, F-35000 Rennes, France
Email: serge.cantat@univ-rennes1.fr

Olga Paris-Romaskevich
Affiliation: Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France
Email: olga@pa-ro.net; olga.romaskevich@math.cnrs.fr

DOI: https://doi.org/10.1090/tran/8229
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