Decay of correlations in expanding semi-flows.
Abstract. I discuss about decay of correlations in suspension semi-flows of angle-multiplying maps on the circle. It has been shown by M. Pollicott (based on Dolgopyat's argment) that, under a mild condition on the ceiling function, the decay rate is exponential. In this talk, I present the following result: under a generic condition on the ceiling function, the Perron-Frobenius operator acting on the anisotropic Sobolev space introduced by V. Baladi and the author has essential spectral radius not greater than the square root of the inverse of the minimal expansion rate. This leads to a precise asymptotic expansion of the correlations.