We extend the persistence results from Lecture 30 and 31 to hyperbolic sets.

Roughly speaking, the moral of the story is the same: if $\Lambda$ is a hyperbolic set for $f$, then if $g$ is close enough to $f$, $g$ will have a hyperbolic set $\Delta$ which is close to $\Lambda$.

Today we assume that such a set $\Delta$ exists, and prove that $\Delta$ is hyperbolic. The existence of such $\Delta$ will come in a few lectures' time.

A screencast of today's lecture is available here.