The name "Thermodynamic formalism" comprises a powerful set of techniques that permit a very fine description of dynamical properties. The sucess of these methods in the context of hyperbolic dynamics is one the major achievements of smooth ergodic theory in the XX century. The problem is that when one relaxes the hyperbolicity hypothesis the panorama becomes much harder to deal with, particularly due to the lack of simple symbolic models.

Together with Federico Rodriguez-Hertz (PSU) we are investigating a different approach to the problem, employing geometrical methods that do not rely on the symbolic description. On the other hand, this new point of view gave us additional perspective in the classical case, allowing us to attack some geometrical problems.

Funding: FAPEMIG UNIVERSAL 28850