Jet dynamics and stability

The dynamics and stability of extragalactic jets may be strongly influenced by small (and probable) di_erences in pressure between the jet and the ambient and within the jet itself. The former give rise to expansion and recollimation of the jet. This occurs in the form of conical shocks, or Mach disks, if the pressure di_erence is large enough. Pressure asymmetries within the jet may trigger the development of helical patterns via coupling to kink current-driven instability, or to helical Kelvin-Helmholtz instability, depending on the physical conditions in the jet. I summarize here the evidence collected during the last years on the presence of recollimation shocks and waves in jets. In the jet of CTA 102 evidence has been found for (traveling)shock-(standing)shock interaction in the core-region (0.1 mas from the core), using information from the light-curve of the source combined with VLBI data. The conclusions derived have been confirmed by numerical simulations combined with emission calculations that have allowed to study the spectral evolution of the perturbed jet. Helical structures can also be identified in radio-jets. The ridge-line of emission of the jet of S5 0836+710 has been identified as a physical structure corresponding to a wave developing in the jet flow. I review here the evidence that has allowed to reach this conclusion, along with an associated caveat. Current data do not allow to distinguish between magnetic or hydrodynamical instabilities. I finally discuss the importance of these linear and non-linear waves for jet evolution