Birational maps with transcendental dynamical degree

2021/07/08 by Jason P. Bell, Jeffrey Diller, Bell, Jason +5 · 2 citations
Mathematics · #11J81 #14E05 (secondary) #32H50 (primary) #37F10 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2107.04113

openalex publication_date 2021/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We give examples of birational selfmaps of ℙ^d, d ≥ 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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