Symplectic non-convexity of toric domains

We inconvexity) of star-shaped toric domains in [Formula: see text]. In particular, based on the criterion from Chaidez–Edtmair [Invent. Math. 229(1) (2022) 243–301] via Ruelle invariant and systolic ratio boundary domains, we provide elementary operations that can kill symplectic convexity. These only result small perturbations terms domains’ volume. Moreover, one is a systematic way to produce examples dynamically convex but not symplectically domains. Finally, are able concrete bounds for constants appear Chaidez–Edtmair’s criterion.