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Fredholm determinants, Anosov maps and Ruelle resonances
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 $\C^\infty$ Anosov diffeomorphisms, the
dynamical determinant is an entire function.