  We introduce a new object, the dynamical torsion, which extends the
potentially ill-defined value at $0$ of the Ruelle zeta function of a contact
Anosov flow twisted by an acyclic representation of the fundamental group. We
show important properties of the dynamical torsion: it is invariant under
deformations among contact Anosov flows, it is holomorphic in the
representation and it has the same logarithmic derivative as some refined
combinatorial torsion of Turaev. This shows that the ratio between this torsion
and the Turaev torsion is locally constant on the space of acyclic
representations.
  In particular, for contact Anosov flows path connected to the geodesic flow
of some hyperbolic manifold among contact Anosov flows, we relate the leading
term of the Laurent expansion of $\zeta$ at the origin, the Reidemeister
torsion and the torsions of the finite dimensional complexes of the generalized
resonant states of both flows for the resonance $0$. This extends previous work
of~\cite{dang2018fried} on the Fried conjecture near geodesic flows of
hyperbolic $3$--manifolds, to hyperbolic manifolds of any odd dimension.
