Birational maps with transcendental dynamical degree

We give examples of birational selfmaps of Pd,d⩾3$\mathbb {P}^d, d \geqslant 3$, whose dynamical degree is a transcendental number. This contradicts a conjecture by Bellon and Viallet. The proof uses a combination of techniques from algebraic dynamics and diophantine approximation.

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Bibliographic Details
Published in:Proceedings of the London Mathematical Society 2024-01, Vol.128 (1), p.n/a, Article Paper No. e12573, 47
Main Authors: Bell, Jason P., Diller, Jeffrey, Jonsson, Mattias, Krieger, Holly
Format: Article
Language:English
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Summary:We give examples of birational selfmaps of Pd,d⩾3$\mathbb {P}^d, d \geqslant 3$, whose dynamical degree is a transcendental number. This contradicts a conjecture by Bellon and Viallet. The proof uses a combination of techniques from algebraic dynamics and diophantine approximation.
ISSN:0024-6115
1460-244X
DOI:10.1112/plms.12573