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arXiv · 1006.5571

On the indices of periodic points in $C^1$-generic wild homoclinic classes in dimension three

Katsutoshi Shinohara
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Abstract

We study the dynamics of homoclinic classes on three dimensional manifolds under the robust absence of dominated splittings. We prove that if such a homoclinic class contains a volume-expanding periodic point, then, $C^1$-generically, it contains a hyperbolic periodic point whose index (dimension of the unstable manifold) is equal to two.

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Katsutoshi Shinohara. 2011-07-19. On the indices of periodic points in $C^1$-generic wild homoclinic classes in dimension three. https://arxiv.org/abs/1006.5571

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