In [Measures of maximal entropy for surface diffeomorphisms][1] appeared in the *Annals*, Buzzi, Crovisier and Sarig proved that (from the Abstract) "$C^\infty$-surface diffeomorphisms with positive topological entropy have finitely many ergodic measures of maximal entropy in general, and exactly one in the topologically transitive case".

Looks like a major result to me, although I'm biased towards dynamical systems.


  [1]: 
https://projecteuclid.org/journals/annals-of-mathematics/volume-195/issue-2/Measures-of-maximal-entropy-for-surface-diffeomorphisms/10.4007/annals.2022.195.2.2.short