TITLE: Phase space structure of multidimensional systems by means of the Mean Exponential Growth factor of Nearby Orbits (MEGNO) AUTHORS: P. M. Cincotta, C. M. Giordano Facultad de Ciencias Astron\'omicas y Geof\'{\i}sicas, Universidad Nacional de La Plata, Paseo del Bosque, 1900 La Plata, Argentina and C. Sim\'o Departament de Matem\`atica Aplicada i An\`alisi, Universitat de Barcelona, Gran Via 585, 08007 Barcelona, Spain E-mail: pmc@fcaglp.unlp.edu.ar, giordano@fcaglp.unlp.edu.ar, carles@maia.ub.es ABSTRACT: In this paper we deal with an alternative technique to study global dynamics in Hamiltonian systems, the Mean Exponential Growth factor of Nearby Orbits, that proves to be efficient to investigate both regular and stochastic components of phase space. It provides a clear picture of resonance structures, location of stable and unstable periodic orbits as well as a measure of hyperbolicity in chaotic domains which coincides with that given by the Lyapunov characteristic number. Here the MEGNO is applied to a 3D perturbed quartic oscillator in order to visualize the structure of its phase space and obtain a quite clear picture of its resonance structure. Examples of application to multidimensional canonical maps are also included. Keywords: Global Dynamics -- Detection of Chaos -- Lyapunov Characteristic Number