Flexible periodic points

We define the notion of epsilon-flexible periodic point: it is a periodic point with stable index equal to two whose dynamics restricted to the stable direction admits epsilon-perturbations both to a homothety and a saddle having an eigenvalue equal to one. We show that an epsilon-perturbation to an epsilon-flexible point allows us to change it to a stable index one periodic point whose (one-dimensional) stable manifold is an arbitrarily chosen C-1-curve. We also show that the existence of flexible points is a general phenomenon among systems with a robustly non-hyperbolic two-dimensional center-stable bundle.