A new paradigm in the logistic and similar maps: time stepping schemes (RACSAM)

We propose the qualitative mathematical analysis of discrete models by replacing the classical Euler scheme of order 1 with Lubich quadrature time-stepping schemes. As the first study with this new paradigm, we compare the bifurcation diagrams for the logistic and sine maps obtained from discretizations of orders 1, 2, and 1/2.