The ordinal of dynamical degrees  of birational maps of the projective plane

Anna Bot

doi:10.5802/crmath.540

Research article - Algebraic geometry, Dynamical systems

The ordinal of dynamical degrees of birational maps of the projective plane

Anna Bot ¹

¹ Department of Mathematics and Computer Science, University of Basel, 4051 Basel, Switzerland

Comptes Rendus. Mathématique, Volume 362 (2024), pp. 117-134.

Abstract
Résumé

We show that the ordinal of the dynamical degrees of all birational maps of the complex projective plane is $ω^{ω}$ .

Nous démontrons que l’ordinal des degrés dynamiques de toutes les transformations birationnelles du plan projectif complexe est $ω^{ω}$ .

Received: 2022-09-01
Revised: 2022-12-09
Accepted: 2023-07-14
Published online: 2024-03-07

DOI: 10.5802/crmath.540

Classification: 37F10, 32H50, 14E07, 14E05
Keywords: Dynamical degree, rational projective surfaces, ordinals

Author's affiliations:

Anna Bot ¹

¹ Department of Mathematics and Computer Science, University of Basel, 4051 Basel, Switzerland

License:

CC-BY 4.0

Copyrights: The authors retain unrestricted copyrights and publishing rights

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     author = {Anna Bot},
     title = {The ordinal of dynamical degrees  of birational maps of the projective plane},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {117--134},
     publisher = {Acad\'emie des sciences, Paris},
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     year = {2024},
     doi = {10.5802/crmath.540},
     language = {en},
}

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Anna Bot. The ordinal of dynamical degrees  of birational maps of the projective plane. Comptes Rendus. Mathématique, Volume 362 (2024), pp. 117-134. doi : 10.5802/crmath.540. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.540/

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