We will discuss a class of volume-contracting surface dieomorphisms (named strong dissipative dieomorphisms) whose dynamics is intermediate between one-dimensional dynamics and general surface dynamics.

For the particular case of the disk, we will consider the ones that have zero entropy, explaining their structure of periodic orbits and showing that they are innitely renormalizable if they are in the boundary of zero entropy.

The talk is a consequence of a series of joint works with Sylvain Crovisier and Charles Tresser