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arXiv · 1605.08000

Global Saddles for Planar Maps

Begoña Alarcón·Sofia B. S. D. Castro·Isabel S. Labouriau
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Abstract

We study the dynamics of planar diffeomorphisms having a unique fixed point that is a hyperbolic local saddle. We obtain sufficient conditions under which the fixed point is a global saddle. We also address the special case of $D_2$-symmetric maps, for which we obtain a similar result for $C^1$ homeomorphisms. Some applications to differential equations are also given.

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Begoña Alarcón, Sofia B. S. D. Castro, Isabel S. Labouriau. 2016-05-25. Global Saddles for Planar Maps. https://arxiv.org/abs/1605.08000

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