MORSE-SMALE SYSTEMS AND HORSESHOES FOR THREE DIMENSIONAL SINGULAR FLOWS

摘要

We prove that every three-dimensional vector field can be C-1 accumulated by Morse-Smale ones, or by ones with a transverse homoclinic intersection of some hyperbolic periodic orbit. In contrast to the case of diffeomorphisms [14], the main difficulty here is that we need to deal with singularities. We also make progress on another conjecture related to Palis in this paper.