Hamiltonian Pseudo-Rotations Of Projective Spaces

Abstract

The main theme of the paper is the dynamics of Hamiltonian diffeomorphisms of CPn with the minimal 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 Poincaré 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.

Publication Date

12-1-2018

Publication Title

Inventiones Mathematicae

Volume

214

Issue

3

Number of Pages

1081-1130

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1007/s00222-018-0818-9

Socpus ID

85053518021 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/85053518021

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