2 problems

ASE-to-NU2SE conjecture. A partially hyperbolic compact invariant set for a smooth flow satisfying the ASE condition (pASE) also satisfies the NU2SE (NUpSE) condition.

Let $S$ be a surface of genus $g=1$, and consider a typical locally Hamiltonian flow preserving a probability measure. Suppose that the flow has at least one periodic component, eq…