# On the dynamics of dominated splitting

### Abstract

Let $f:M\to M$ be a $C^2$ diffeomorphism of a compact surface. We give a complete description of the dynamics of any compact invariant set having dominated splitting. In particular, we prove a Spectral Decomposition Theorem for the limit set $L(f)$ under the assumption of dominated splitting. Moreover, we describe all the bifurcations that these systems can exhibit and the different types of dynamics that could follow for small $C^r-$perturbations.

## Authors

Enrique R. Pujals

Instituto de Matemática Pura e Aplicada
22460-320 Rio de Janeiro, R.J.
Brazil

Martín Sambarino

Facultad de Ciencias - Centro de Matemática
Universidad de la República
11400 Montevideo
Uruguay