Constructing invariant tori using guaranteed Euler method

TL;DR

This paper presents a method using Euler's integration and error bounding functions to construct structures that closely surround invariant tori in dynamical systems, accounting for small perturbations.

Contribution

It introduces a novel approach combining Euler's method with error bounds to generate invariant torus structures in dynamical systems.

Findings

Structures closely surrounding invariant tori are constructed.

The method accounts for deformations under small perturbations.

Finite collections of balls in b^n are used to represent the tori.

Abstract

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.