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arXiv · 1702.05994

Homoclinic tangencies and singular hyperbolicity for three-dimensional vector fields

Sylvain Crovisier·Dawei Yang
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Abstract

We prove that any vector field on a three-dimensional compact manifold can be approximated in the C1-topology by one which is singular hyperbolic or by one which exhibits a homoclinic tangency associated to a regular hyperbolic periodic orbit. This answers a conjecture by Palis. During the proof we obtain several other results with independent interest: a compactification of the rescaled sectional Poincar\'e flow and a generalization of Ma\~n\'e-Pujals-Sambarino theorem for three-dimensional C2 vector fields with singularities.

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Sylvain Crovisier, Dawei Yang. 2017-02-20. Homoclinic tangencies and singular hyperbolicity for three-dimensional vector fields. https://arxiv.org/abs/1702.05994

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