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