An example of $C^1$-generically wild homoclinic classes with index deficiency

Mathematics – Dynamical Systems

Scientific paper

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Scientific paper

10.1088/0951-7715/24/7/003

Given a closed smooth four-dimensional manifold, we construct a
diffeomorphism that has a homoclinic class whose continuation locally
generically satisfies the following condition: it does not admit any kind of
dominated splittings whereas any periodic points belonging to it never have
unstable index one.

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