Let $f:M\rightarrow M$ be a biholomorphisms on two--dimensional a complex
manifold, and let $X\subseteq M$ be a compact $f$--invariant set such that
$f|X$ is asymptotically dissipative and without sinks periodic points. We
introduce a solely dynamical obstruction to dominated splitting, namely
critical point. Critical point is a dynamical object and capture many of the
dynamical properties of their one--dimensional counterpart.