On the structure of symplectic mappings. The fast Lyapunov indicator: A very sensitive tool

It is already known (Froeschle, Lega and Gonczi, 1997) that the Fast Lyapun ov Indicator (FLI), that is the computation on a relatively short time of t he largest Lyapunov indicator, allows to discriminate between ordered and w eak chaotic motion. We have found that, under certain conditions, the FLI a lso discriminates between resonant and non-resonant orbits, not only for tw o-dimensional symplectic mappings but also for higher dimensional ones. Usi ng this indicator, we present an example of the Arnold web detection for fo ur and six-dimensional symplectic maps. We show that this method allows to detect the global transition of the system from an exponentially stable Nek horoshev's like regime to the diffusive Chirikov's one.