  In the first part of this dissertation, we give a new definition of a Laplace
operator for Finsler metric as an average, with regard to an angle measure, of
the second directional derivatives. This operator is elliptic, symmetric with
respect to the Holmes-Thompson volume, and coincides with the usual
Laplace--Beltrami operator when the Finsler metric is Riemannian. We compute
explicit spectral data for some Katok-Ziller metrics. When the Finsler metric
is negatively curved, we show, thanks to a result of Ancona that the Martin
boundary is H\"older-homeomorphic to the visual boundary. This allow us to
deduce the existence of harmonic measures and some ergodic preoperties. In the
second part of this dissertation, we study Anosov flows in 3-manifolds, with
leaf-spaces homeomorphic to $\mathbb{R}$. When the manifold is hyperbolic,
Thurston showed that the (un)stable foliations induces a regulating flow. We
use this second flow to study isotopy class of periodic orbits of the Anosov
flow and existence of embedded cylinders.
