# Homoclinic tangencies and hyperbolicity for surface diffeomorphisms

### Abstract

We prove here that in the complement of the closure of the hyperbolic surface diffeomorphisms, the ones exhibiting a homoclinic tangency are $C^1$ dense. This represents a step towards the global understanding of dynamics of surface diffeomorphisms.

## Authors

Enrique R. Pujals

Martín Sambarino