Birational maps with transcendental dynamical degree

We give examples of birational selfmaps of $\mathbb{P}^d, d \geq 3$, 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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Bibliographische Detailangaben
Hauptverfasser:	Bell, Jason, Diller, Jeffrey, Jonsson, Mattias, Krieger, Holly
Format:	Artikel
Sprache:	eng
Schlagworte:	Mathematics - Algebraic Geometry Mathematics - Dynamical Systems Mathematics - Number Theory
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Beschreibung
Zusammenfassung:	We give examples of birational selfmaps of $\mathbb{P}^d, d \geq 3$, 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.
DOI:	10.48550/arxiv.2107.04113