Year: 2011
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Author: Valenzuela, Francisco
Institution: Pontificia Universidad Católica de Valparaíso
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W1624942240