  The content of this contribution is based on the course on numerical analysis
techniques for non-linear dynamics. After introducing basic concepts as the
visual analysis of trajectories in phase space and the importance of the nature
of fixed points in their topology and dynamics, the motion close to a resonance
is presented, with simple non-linear map examples. The onset of chaotic motion
and the modern methods used for their detection are detailed with a focus on
frequency map analysis and concrete examples for a variety of rings and
non-linear effects.
