Let $f: [0,1] \to [0,1]$ be an infinitely renormalizable unimodal map, let $c$ denote its critical point. It is well-known that the post-critical set $\omega(c)$ of $f$ (which is the omega limit set of $c$) is a minimal Cantor set and is a global attractor in both metric and topological sense. Such a map has a unique physical measure $\mu$ supported on $\omega(c)$ and $f|\omega(c)$ is uniquely ergodic.
My question is: let orb(c) denote the set of the forward orbits of $c$, does $\mu(orb(c))=1$?