Georgia Institute of Technology College of Sciences

In this talk I will generalize a simple trick to produce splitting for the separatrices of (the time-one map of) a simple pendulum, to hyperbolic tori of any dimension $m\geq 2$. The examples will be constructed in the Gevrey class, and the splitting is bounded from below by a term of the form $\exp (-c(1/\eps)^a)$, where $a=\frac{1}{2(\alpha-1)(m-2)}$. This will be compared to usual upper bounds in the same setting.