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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48 .

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Automorphisms of compact Kähler manifolds with slow dynamics
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by Serge Cantat and Olga Paris-Romaskevich PDF
Trans. Amer. Math. Soc. 374 (2021), 1351-1389 Request permission


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
  • Email:
  • Olga Paris-Romaskevich
  • Affiliation: Aix Marseille Univ, CNRS, Centrale Marseille, I2M, Marseille, France
  • MR Author ID: 1078211
  • Email:;
  • 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
  • © Copyright 2020 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 374 (2021), 1351-1389
  • MSC (2020): Primary 14H37, 37A35
  • DOI:
  • MathSciNet review: 4196396