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

Abstract

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.

References in corpus (1)

• Recurrence and genericity

Cited by in corpus (2)

• Stabilization of heterodimensional cycles
• Super exponential divergence of periodic points for C^1-generic partially hyperbolic homoclinic classes