Pseudo-rotations and holomorphic curves

We prove a variant of the Chance–McDuff conjecture for pseudo-rotations: under certain additional conditions, a closed symplectic manifold which admits a Hamiltonian pseudo-rotation must have deformed quantum product and, in particular, some non-zero Gromov–Witten invariants. The only assumptions on the manifold are that it is weakly monotone and that its minimal Chern number is at least two. The conditions on the pseudo-rotation are expressed in terms of the linearized flow at one of the fixed points and are hypothetically satisfied for most (but not all) pseudo-rotations.