Axiom-A realization of every quotient

Determine whether every quotient set L(g) arising from a representative of a pseudo-Anosov isotopy class is realized by an Axiom-A representative; equivalently, determine whether every ≈-equivalence class contains an Axiom-A homeomorphism or diffeomorphism.

Background

The quotient sets L(g) classify representatives under the relation g≈g′ when they coincide. The appendix asks whether these quotient classes can always be represented by uniformly hyperbolic Axiom-A dynamics, which would provide a strong structural realization result for the global orbit quotients.

References

Is every $L(g)$ realized by some Axiom A? That is, does every $\approx$-class contain an Axiom A?

— Entropy and periodic points in pseudo-Anosov isotopy classes  (2610.26230 - Carrasco et al., 19 Oct 2026) in Appendix, Section “Questions {content} Comments”