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

I explore the concrete applicability of recent theoretical results to the rigorous computation of relevant statistical properties of a simple class of dynamical systems: piecewise expanding maps 1 Introduction The aim of the present paper is to investigate the possibility of answering questions of the type: ffl Given a piecewise expanding map is it possible to decide if it is ergodic or mixing? ffl Is it possible to determine with arbitrary precision its absolutely continuous invariant measure? ffl If the map is mixing, is it possible to compute the exact rate of decay of correlations for a given function? Of course, the literature contains many papers in which some of these question are discussed either theoretically (especially, but not exclusively, as far as the invariant density is concerned) or numerically (e.g. [3], [4, 5, 6, 7], [8, 9], [14], [15], [18, 19], [21, 22], [23, 24, 25], [27, 28, 29, 30, 31, 32, 33], [34, 35], [38], [39, 40], [48], [49], [52], [55], [62], [66]). N...