  I show that the dynamical determinant, associated to an Anosov
diffeomorphism, is the Fredholm determinant of the corresponding
Ruelle-Perron-Frobenius transfer operator acting on appropriate Banach spaces.
As a consequence it follows, for example, that the zeroes of the dynamical
determinant describe the eigenvalues of the transfer operator and the Ruelle
resonances and that, for $\Co^\infty$ Anosov diffeomorphisms, the dynamical
determinant is an entire function.
