## Vilton Pinheiro

### Abstract:

In the first lecture we will talk about the problem of lifting a measure to an induced map. We will give a necessary and sufficient condition for a measure to be liftable as well as a condition for the lift to be ergodic and unique.

The second lecture will be dedicated to construct induced maps well adapted to a given ergodic invariant probability with all its Lyapunov exponents being positive (expanding measure).

Finally, in the third lecture, we will discuss about equilibrium states on the support of an ergodic invariant expanding probability. In particular, (1) we will show that Viana maps have one and only one probability maximizing their entropy and (2) we will analyze the existence and uniqueness of the equilibrium states for Hölder potentials at high temperature.

## About the author