Emergence of partially hyperbolic skew-products with circle fibers

We study the statistical behavior of partially hyperbolic skew-products over Axiom A diffeomorphisms using emergence. Generically, these systems satisfy the Palis conjecture: they have a finite number of physical measures whose basins together have full volume. In particular, for Lebesgue almost every point, the empirical measures converge to one of finitely many physical measures. We study the non-generic case and prove that, even when the sequence of empirical measures may have uncountably many accumulation points, these systems have low emergence.