Morse-Smale systems and horseshoes for three dimensional singular flows

By Shaobo Gan, Dawei Yang. 2013

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We prove that for every three-dimensional vector field, either it can be accumulated by Morse-Smale ones, or it can be accumulated by ones with a transverse homoclinic intersection of some hyperbolic periodic orbit in the $C^1$ topology.

Subfields: Geometry and Topology, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f74886528bab258bd46621c1b66091b70a0670b9