Sommerfeld condition for a Liouvilleequation and concentration of trajectories

We analyse the concentration of trajectories in aLiouville equation set in the full space with a potential whichis not constant at infinity. Our motivation comes fromgeometrical optics where it appears as the high freqency limitof Helmholtz equation. We conjecture that the mass and energyconcentrate on local maxima of the refraction index and prove aresult in this direction. To do so, we establish a prioriestimates in appropriate weighted spaces and various forms of aSommerfeld radiation condition for solutions of such astationary Liouville equation.Dedicated to IMPA on the occasion of its 50^th anniversary