  Frequency Map Analysis is a numerical method based on refined Fourier
techniques which provides a clear representation of the global dynamics of many
multi-dimensional systems, and which is particularly adapted for systems of
3-degrees of freedom and more. This method relies heavily on the possibility of
making accurate quasiperiodic approximations of of quasiperiodic signal given
in a numerical way. In the present paper, we will describe the basis of the
frequency analysis method, focussing on the quasi periodic approximation
techniques. Application of these methods for the study of the global dynamics
and chaotic diffusion of Hamiltonian systems and symplectic maps in different
domains can be found in (Laskar, 1988, 1990, Laskar and Robutel, 1993, Robutel
and Laskar, 2001, Nesvorny and Ferraz-Mello, 1997) for solar system dynamics,
and in (Papaphilippou and Laskar, 1996, 1998, Laskar, 2000, Wachlin and
Ferraz-Mello, 1998, Valluri and Merritt, 1998, Merritt and Valluri, 1999) for
galactic dynamics. The method has been particularly successful for its
application in particle accelerators (Dumas and Laskar, 1993, Laskar and Robin,
1996, Robin et al., 2000, Comunian et al., 2001, Papaphilippou and Zimmermann,
2002, Steier et al., 2002), and was also used for the understanding of atomic
physics (Milczewski et al., 1997), or more general dynamical system issues
(Laskar et al., 1992, Laskar, 1993, 1999, Chandre et al., 2001).
