5 problems

A pseudo-rotation is a Hamiltonian system, Hamiltonian diffeomorphism, or Reeb flow with finitely many periodic orbits. Anosov–Katok realization conjecture. All pseudo-rotations ar…

Let $(M,\omega)$ be a monotone symplectic manifold admitting a pseudo-rotation. Here $\gamma_\mathbb{Z}$ denotes the spectral norm over the integers, and $\phi^k$ denotes the $k$-t…

Let $S$ be an orientable analytic surface. An analytic symplectomorphism of the sphere with only two fixed points and no other periodic point, or of a compact cylinder without peri…

Balanced pseudo-rotation conjecture. Every pseudo-rotation of $\mathbb{C}P^n$ is balanced.

Let $\varphi$ be a pseudo-rotation of $\mathbb{C}P^n$ with mean index vector $\Delta$. The vector $\Delta$ is exponentially Liouville when it satisfies the exponential approximatio…