Rational Surface Automorphisms with Positive Entropy
Annales de l'Institut Fourier, Volume 66 (2016) no. 1, p. 377-432

The aim of this paper is to construct rational surface automorphisms with positive entropy by means of the concept of orbit data. The concept enables us to introduce some mild and verifiable condition, and to show that if an orbit data satisfies the condition, then there exists an automorphism realizing the orbit data. Applying this result, we describe the set of entropy values of the rational surface automorphisms in terms of Weyl groups.

Le but de ce travail est de construire des automorphismes de surfaces rationnelles d’entropie positive au moyen de la notion de donnée d’orbite. Celle-ci nous permet d’introduire une condition faible et vérifiable, et de démontrer que si une donnée d’orbite satisfait cette condition, alors il existe un automorphisme qui réalise la donnée d’orbite. En appliquant ce résultat, nous décrivons l’ensemble des valeurs d’entropie des automorphismes de surfaces rationnelles du point de vue des groupes de Weyl.

Received : 2013-07-25
Revised : 2015-05-14
Accepted : 2015-06-11
Published online : 2016-02-17
DOI : https://doi.org/10.5802/aif.3014
Classification:  14E07,  14J50,  37F99
Keywords: rational surface, automorphism, entropy, orbit data
     author = {Uehara, Takato},
     title = {Rational Surface Automorphisms  with Positive Entropy},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {66},
     number = {1},
     year = {2016},
     pages = {377-432},
     doi = {10.5802/aif.3014},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2016__66_1_377_0}
Uehara, Takato. Rational Surface Automorphisms  with Positive Entropy. Annales de l'Institut Fourier, Volume 66 (2016) no. 1, pp. 377-432. doi : 10.5802/aif.3014. http://www.numdam.org/item/AIF_2016__66_1_377_0/

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