  Let $X_0$ be a smooth projective threefold which is Fano or which has Picard
number $1$. Let $\pi :X\rightarrow X_0$ be a finite composition of blowups
along smooth centers. We show that for "almost all" of such $X$, if $f\in
Aut(X)$ then its first and second dynamical degrees are the same. We also
construct many examples of finite blowups $X\rightarrow X_0$, on which any
automorphism is of zero entropy.
  The main idea is that because of the log-concavity of dynamical systems and
the invariance of Chern classes under holomorphic automorphisms, there are some
constraints on the nef cohomology classes.
  We will also discuss a possible application of these results to a threefold
constructed by Kenji Ueno.
