Among smooth Anosov flows on 3-manifolds preserving a smooth volume,
algebraic models are believed to distinguish themselves in many ways.
The question of entropy rigidity asks whether algebraic models can be characterized
(up to smooth conjugacy) by the property that the volume measure has maximal entropy.
I will present some results in this direction obtained in a joint project with
J. De Simoi, K. Vinhage and Y. Yang.
We shall see that a key step is to obtain precise estimates
on the Lyapunov exponents of periodic orbits with a prescribed combinatorics.
We will also present some results towards the question of entropy rigidity for dispersing billiards.