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Waves Are Recurrent on Noncompact Fractals

Research paper by Robert S. Strichartz

Indexed on: 16 Oct '09Published on: 16 Oct '09Published in: Journal of Fourier Analysis and Applications



Abstract

On certain noncompact fractals there exist Laplacians with pure point spectrum. It follows that solutions of the wave equation, the free Schrödinger 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.