Threshold dynamics for the 3$d$ radial NLS with combined nonlinearity

We consider the nonlinear Schrödinger equation with focusing quintic and defocusing cubic nonlinearity in three space dimensions: $$(i{\mathrm{\partial }}_t+\mathrm{\Delta })u=\mathrm{\mid }u{\mathrm{\mid }}^{2}u-\mathrm{\mid }u{\mathrm{\mid }}^{4}u\mathrm{.}$$ In [18, 23], the authors classified the dynamics of solutions under the energy constraint $E(u)<E^c(W)$, where $W$ is the quintic NLS ground state and $E^c$ is the quintic NLS energy. In this work we classify the dynamics of $H^1$ solutions at the threshold $E(u)=E^c(W)$.