Flexible periodic points

Abstract

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 $\epsilon$-perturbation to an $\epsilon$-flexible point allows to change it in 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 point is a general phenomenon among systems with a robustly non-hyperbolic two dimensional center-stable bundle.

References in corpus (4)

• Recurrence and genericity
• Stabilization of heterodimensional cycles
• Perturbation of the Lyapunov spectra of periodic orbits
• A Franks' lemma that preserves invariant manifolds

Cited by in corpus (2)

• Volume hyperbolicity and wildness
• A mechanism for ejecting a horseshoe from a partially hyperbolic chain recurrence class