Non-ergodicity on SU(2) and SU(3) character varieties of the once-punctured torus

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

Publication date: 28 June 2022

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

Has companion code repository: https://github.com/seanlawton/Non-ergodicity-on-SU-2-and-SU-3-character-varieties-of-the-once-punctured-torus

Mathematics Subject Classification ID

Ergodicity, mixing, rates of mixing (37A25) Ergodic theory on groups (22D40) Symplectic structures of moduli spaces (53D30) Nearly integrable Hamiltonian systems, KAM theory (70H08) Character varieties (14M35)

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