Periodic approximations of irrational pseudo-rotations using pseudoholomorphic curves

• 成果类型: Article
• 署名作者: Bramham, Barney
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2015.181.3.4
• 发表日期: 2015
• 页码: 1033-1086
• 关键词: holomorphic-curves; tight 3-sphere; annulus; DYNAMICS; symplectisations; symplectizations; diffeomorphisms; foliations; MANIFOLDS; SURFACES

摘要

We prove that every C-infinity-srnooth, area preserving diffeomorphisrn of the closed 2-disk having not more than one periodic point is the uniform limit of periodic C-infinity-srnooth diffeomorphisrns. In particular, every smooth irrational pseudo-rotation can be C-0-approximated by integrable systems. This partially answers a long standing question of A. Katok regarding zero entropy Hamiltonian systems in low dimensions. Our approach uses pseudoholomorphic curve techniques from symplectic geometry.