Analytic pseudo-rotations II: a principle for spheres, disks and annuli

2024/02/23 by Pierre Berger, Berger, Pierre · 2 citations
Engineering · #Dynamical Systems (math.DS) #FOS: Mathematics #Geophysics and Sensor Technology

paper · pdf · doi:10.48550/arxiv.2402.15303

openalex publication_date 2024/02/23 · openalex created_date 2024/02/27 · openalex updated_date 2026/07/28

Abstract

We construct analytic surface symplectomorphisms with unstable elliptic fixed points; this solves a problem of Birkhoff (1927). More precisely, we construct analytic symplectomorphisms of the sphere and of the disk which are transitive, with respectively only 2 and 1 periodic points. This also solves problems of proposed by Herman (1998), Fayad-Katok (2004) and Fayad-Krikorian (2018). To establish these results, we introduce a principle that enables to realize, by an analytic symplectomorphism, properties which are C⁰-realizable by the approximation by conjugacy method of Anosov-Katok.

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• Wild dynamics on manifolds
• Analytic pseudo-rotations displaying ergodicity or emergence on the sphere and disk

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