On the numerical computation of orbits of dynamical systems: The one- dimensional case (Q805837)

Due to roundoff error the numerically computed orbits of dynamical systems are pseudo-orbits rather than true orbits. This article presents a practical procedure which allows to estimate how far a pseudo-orbit is from an exact orbit (for one-dimensional maps). The quality of the obtained estimates is illustrated at the iteration \(x_{n+1}=f(x_ n)\) where f is the quadratic map \(f(x)=3.8x(1-x)\).