Constructing Invariant Tori Using Guaranteed Euler Method

We show here how, using Euler's integration method and an associated function bounding the error in function of time, one can generate structures closely surrounding the invariant tori of dynamical systems. Such structures are constructed from a finite number of balls of $\mathbb{R}^n$ and encompass the deformations of the tori when small perturbations of the flow of the system occur.