Quantitative symplectic topology of Katok's examples and equivariant symplectic embeddings

The Katok examples on $S^2$ are induced by Randers metrics obtained by perturbing the round metric by the standard rotational Killing field: allowing a scaling factor of the round metric gives a two-parameter family of Randers metrics $F_{α,β}$, parametrised by positive real numbers $(α,β)$. We comp