Minimal representative in each quotient class

Determine whether every ≈-equivalence class of representatives with the same quotient L(g) contains a representative minimizing a specified complexity measure, such as the number of periodic points or topological entropy.

Background

Representatives with the same quotient set need not be known to be semiconjugate, and the quotient captures only part of their dynamics. The appendix asks whether one can choose a dynamically minimal representative within each class, including with respect to periodic-point count or topological entropy.

References

Is there a minimal representative (e.g. in the sense of its number of periodic points, topological entropy, etc.) in each $\approx$-class?

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