Coarse Distance from Dynamically Convex to Convex

Chaidez and Edtmair have recently found the first examples of dynamically convex domains in R4 that are not symplectomorphic to convex domains (called symplectically convex domains), answering a long-standing open question. In this talk we shall present new examples of such domains without referring to Chaidez-Edtmair’s criterion. We shall show that these domains are arbitrarily far from the set of symplectically convex domains in R4

 with respect to the coarse symplectic Banach-Mazur distance by using an explicit numerical criterion for symplectic non-convexity. This is joint work with J.Dardennes, V.Ramos and J.Zhang