
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
