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.



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