Non-ergodicity on $\mathrm{SU}\left(2\right)$ and $\mathrm{SU}\left(3\right)$ character varieties of the once-punctured torus

Forni, Giovanni; Goldman, William M.; Lawton, Sean; Matheus, Carlos

Annales Henri Lebesgue, Tome 7 (2024), pp. 1099-1130

Utilizing KAM theory, we show that there are certain levels in relative $\mathrm{SU}\left(2\right)$ and $\mathrm{SU}\left(3\right)$ character varieties of the once-punctured torus where the action of a single hyperbolic element is not ergodic.

En utilisant la théorie KAM, on montre l’existence de certains niveaux dans les variétés de caractères relatives pour $\mathrm{SU}\left(2\right)$ et $\mathrm{SU}\left(3\right)$ d’un tore épointé sur lesquels l’action d’un élément hyperbolique spécifique n’est pas ergodique.

Classification : 14M35, 22D40, 70H08, 53D30, 37A25
Keywords: KAM Theory, Non-ergodicity, Character Variety

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