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

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

2010-06-29

arxiv.org/abs/1006.5571v2

Mathematics

Dynamical Systems

To appear in DCDS-A

Scientific paper

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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