The Anosov–Katok method and pseudo-rotations in symplectic dynamics

We prove that toric symplectic manifolds admit Hamiltonian pseudo-rotations with a finite, and in a sense minimal, number of ergodic measures. The set of ergodic measures of these pseudo-rotations consists of the measure induced by the symplectic volume form and the Dirac measures supported at the f...

Full description

Saved in:
Bibliographic Details
Published in:Journal of fixed point theory and applications Vol. 24; no. 2
Main Authors: Le Roux, Frédéric, Seyfaddini, Sobhan
Format: Journal Article
Language:English
Published: Cham Springer International Publishing 01.06.2022
Springer Verlag
Subjects:
Analysis
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Physics
Symplectic geometry - A Festschrift in honour of Claude Viterbo’s 60th birthday
53D05
symplectic dynamics
unique ergodicity
pseudo rotations
Anosov–Katok method
37C05
Anosov-Katok method
Unique ergodicity
Symplectic dynamics
Pseudo rotations
ISSN:1661-7738, 1661-7746
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We prove that toric symplectic manifolds admit Hamiltonian pseudo-rotations with a finite, and in a sense minimal, number of ergodic measures. The set of ergodic measures of these pseudo-rotations consists of the measure induced by the symplectic volume form and the Dirac measures supported at the fixed points of the torus action. Our construction relies on the conjugation method of Anosov and Katok.
ISSN:1661-7738
1661-7746
DOI:10.1007/s11784-022-00955-8