From hyperbolicity to dominated splitting
Enrique R. Pujals
In this survey, we show a series of dynamical contexts where the notion of dominated splitting appears naturally. In particular, we show how it extends the notion of hyperbolicity and explains robust dynamical phenomena that are not hyperbolic. On the other hand, we expose how the dominated splitting helps us to find hyperbolic structures: in fact, we show that in certain cases, the dominated splitting structure arises naturally and from there hyperbolicity is concluded. To attain this last kind of result, we expose a series of theorems that explain the dynamical consequences that follow from a dominated splitting.