Waves are recurrent on noncompact fractals

摘要

On certain noncompact fractals there exist Laplacians with pure point spectrum. It follows that solutions of the wave equation, the free Schr?dinger equation or the Klein-Gordon equation based on these Laplacians are essentially almost periodic functions of time, so the same values will recur to within any prescribed error. Also, to within any prescribed error, the solution has compact support in space for all time.