Theory and Applications of the Mean Exponential Growth Factor of Nearby Orbits (MEGNO) Method

In this chapter we discuss in a pedagogical way and from the very beginning the Mean Exponential Growth factor of Nearby Orbits (MEGNO) method, that has proven, in the last ten years, to be efficient to investigate both regular and chaotic components of phase space of a Hamiltonian system. It is a fast indicator that provides a clear picture of the resonance structure, the location of stable and unstable periodic orbits as well as a measure of hyperbolicity in chaotic domains which coincides with that given by the maximum Lyapunov characteristic exponent but in a shorter evolution time. Applications of the MEGNO to simple discrete and continuous dynamical systems are discussed and an overview of the stability studies present in the literature encompassing quite different dynamical systems is provided.