Analytic pseudo-rotations

• 成果类型: Article
• 署名作者: Berger, Pierre
• 署名单位: Centre National de la Recherche Scientifique (CNRS); Sorbonne Universite; Universite Paris Cite
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X; 1939-8980
• DOI: 10.4007/annals.2026.204.1.3
• 发表日期: 2026-07
• 页码: 221-263
• 关键词: Birkhoff's conjecture; Anosov-Katok; pseudo-rotation; quasi-periodic dynamics; symplectic dynamics; analytic dynamics; surface dynamics; emergence; constructions

摘要

We construct analytic symplectomorphisms of the cylinder or the sphere with zero or exactly two periodic points that are not conjugate to a rotation. In the case of the cylinder, we show that these symplectomorphisms can be chosen to be ergodic or, to the contrary, with local emergence of maximal order. In particular, this disproves a conjecture of Birkhoff (1941) and solves a problem of Herman (1998). One aspect of the proof provides a new approximation theorem; it enables the implementation of the Anosov- Katok scheme in new analytic settings.