Vitesse de convergence vers l'état d'équilibre pour des dynamiques markoviennes non höldériennes

We study the convergence speed to equilibrium state for Markovian non hölderian dynamics. In particular, an estimation of the mixing speed is obtained on a subspace B which is dense in the space of continuous functions. Moreover, we show that the spectrum of the Perron-Frobenius operator as acting on B is a whole elosed disk of which each point is an eigenvalue. This implies that the convergence speed cannot be exponential.