Organization of chaos in area-preserving maps

Chaos in area-preserving maps is organized on the basis of the unstable periodic orbits (UPOs) and the partition of phase space into resonances. Each UPO is of a well defined type, which specifies the sequence of resonances visited and the number of rotations performed in a resonance. Chaotic orbits are grouped into sets of well defined type, topological and metric characterizations. The effect of regular motion on global diffusion may be characterized by an infinity of diffusion coefficients, associated with ensembles of chaotic orbits that are trapped in extended sets of resonances.