| Contents |
| In this talk I will discuss extensively the use of dynamical indicators
that have proven to be efficient to investigate both regular
and chaotic components of phase space of Hamiltonian systems.
As it will be shown, they provide 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. Moreover, most dynamical
indicators, based on the evolution of the so-called deviation vectors, are suitable to
reveal the extremely thin chaotic layers around resonances and therefore,
to investigate numerically the \emph{diffusion} along a single resonance (Arnold diffusion?).
Applications to discrete and continuous systems will be addressed, as well as an overview
of the stability studies present in the literature encompassing quite different dynamical
systems will be provided. |
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