On Critical Point for Two Dimensional Holomorphics Systems

الأصل · EN

Let f:M→ M be a biholomorphisms on two--dimensional a complex manifold, and let X 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.