  We study linear inhomogeneous kinetic equations with an external confining
potential and a collision operator admitting several local conservation laws
(local density, momentum and energy). We classify all special macroscopic modes
(stationary solutions and time-periodic solutions). We also prove the
convergence of all solutions of the evolution equation to such non-trivial
modes, with a quantitative exponential rate. This is the first hypocoercivity
result with multiple special macroscopic modes with constructive estimates
depending on the geometry of the potential.
