We prove that all star vector fields, including Lorenz attractors and multisingular hyperbolic vector fields, admit the intermediate entropy property. To be precise, if $X$ is a star vector field with $h_{ top}(X)>0$, then for any $h\in [0,h_{ top}(X))$, there exists an ergodic invariant measure $\mu$ of $X$ such that $h_{ \mu}(X)=h$. Moreover, we show that the topological entropy is lower semi-continuous for star vector fields.
Categories: math.DS