Rigorous numerical investigation of the statistical properties of piecewise expanding maps. A feasibility study (Q2722666)

Let \(T:[0,1]\rightarrow [0,1]\) be a piecewise \(C^{(2)}\) map. The author makes a theoretical numerical study for answering questions of the type: when is \(T\) expanding? or if \(T\) is expanding, when can we say that it is ergodic or mixing and determine precisely the absolutely continuous invariant measure? The starting point is the Ruelle-Perron-Frobenius operator of the map \(T\) and the methods developed by the author are based on it. The paper is self-contained and includes a lot of related bibliography.