01-114 Sebastien Gouezel
spectre de l'op{\'e}rateur de transfert en dimension 1 (500K, Postscript) Mar 28, 01
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Abstract. We study the spectral properties of a transfer operator $\mathcal{M}\Phi(x)=\sum_{\omega}g_{\omega}(x)\Phi(\psi_\omega x)$ acting on functions of bounded variation. After estimations - using a symetrical integral - of the spectral radius and of the essential spectral radius, we consider the dynamical determinant $\Det^\#(\Id+z\boM)$. We generalize to the case of discontinuous weights the results of Baladi and Ruelle (for continuous weights) on the link between zeros of the sharp determinant and eigenvalues of the transfer operator. The proof, by regularization of the weights, uses a spectral result giving the surjectivity of some applications between eigenspaces of operators.

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