马蹄的存在蕴含横截同宿点的存在

The Existence of Horseshoe Contains the Existence of Transverse Homoclinic Point

对于微分同胚 ,横截同宿点的存在蕴含 Smale马蹄的存在 .本文证明了这一定理的逆定理成立 ,即 Smale马蹄的存在也蕴含横截同宿点的存在 .

For a diffeomorphism, the existence of transverse homoclinic point contain the existence of Smale horseshoe. In this paper, we prove that it′s converse theorem is hold, that is, the existence of horseshoe contain the existence of transverse homoclinic point.