Numerical estimates of local dimension by waiting time and quantitative recurrence

Waiting time indicators are defined by measuring the time needed for a point x to approach a given point y. Our aim is to test the use of waiting time indicators, and quantitative recurrence ones to numerically estimate the local dimension of attractors in dynamical systems, as suggested by some rigorous results. We test this approach on a collection of examples, whose dimensions are already known rigorously, or with a large amount of precision. The main outcome is that the use of waiting time, compared to recurrence increases largely the speed of convergence of the estimators.