Hamiltonian pseudo-rotations of projective spaces

• 成果类型: Article
• 署名作者: Ginzburg, Viktor L.; Gurel, Basak Z.
• 署名单位: State University System of Florida; University of Central Florida; University of California System; University of California Santa Cruz
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-018-0818-9
• 发表日期: 2018
• 页码: 1081-1130
• 关键词: noncontractile periodic-orbits; fixed-point theorem; index; DYNAMICS; homeomorphisms; geometry; systems; energy

摘要

Themain theme of the paper is the dynamics of Hamiltonian diffeomorphisms of CPn with theminimal possible number of periodic points (equal to n + 1 by Arnold's conjecture), called here Hamiltonian pseudo-rotations. We prove several results on the dynamics of pseudo-rotations going beyond periodic orbits, using Floer theoretical methods. One of these results is the existence of invariant sets in arbitrarily small punctured neighborhoods of the fixed points, partially extending a theorem of Le Calvez and Yoccoz and of Franks and Misiurewicz to higher dimensions. The other is a strong variant of the Lagrangian Poincare recurrence conjecture for pseudo-rotations. We also prove the C0-rigidity of pseudo-rotations with exponentially Liouville mean index vector. This is a higher-dimensional counterpart of a theorem of Bramham establishing such rigidity for pseudo-rotations of the disk.