The diffusion coefficient for piecewise expanding maps of the interval with metastable states (Q2888810)

The authors study the number of ergodic absolutely continuous invariant probability measures.NEWLINENEWLINEThe first main result (Theorem 1) states that distributions of jumps of the systems converge to the finite-dimensional distributions of the Markov chain.NEWLINENEWLINEThe second main result (Theorem 2) states that, for any observable \(A\) with bounded variation, \(\varepsilon D_{\varepsilon} (A)\rightarrow \mathbf{D}^M (\mathbf{A})\) as \(\varepsilon \rightarrow 0\), where \(\mathbf{A}\) is the observable on the state space of the Markov chain with \(\mathbf{A} (j)=\int_{I_j} A{\phi}_j dx\) and \(\mathbf{D}^M\) is the diffusion coefficient.