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...

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Vydané v:Journal of fixed point theory and applications Ročník 24; číslo 2
Hlavní autori: Le Roux, Frédéric, Seyfaddini, Sobhan
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: Cham Springer International Publishing 01.06.2022
Springer Verlag
Predmet:
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
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Popis
Shrnutí: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