Decay of Correlations for the Manneville-Pommeau Map
Maneville-Pomeau map, Invariant Cones, Perron-Frobenius Operator, Polynomial decay of correlations
In this work, we will study ergodic properties of the Maneville-Poumeau Map. More precisely, we will prove that such dynamics has an invariant probability, equivalent to the Lebesgue measure, whose density is locally Lipschitz. We will also prove that such a transformation has polynomial decay of correlations over the space L∞ and C1. To obtain the first result, we will build cones, with compactness properties, invariant by the action of the Transfer operator. For the second, we will use operator perturbation techniques. The results obtained in this work were developed by C. Liverani, B. Saussol and S. Vaienti in [5].