Mixing in an anharmonic potential well

Abstract

We prove phase-space mixing for solutions to Liouville's equation for integrable systems. Under a natural non-harmonicity condition, we obtain weak convergence of the distribution function with rate $⟨\mathrm{time}{⟩}^{-1}$. In one dimension, we also study the case where this condition fails at a certain energy, showing that mixing still holds but with a slower rate. When the condition holds and functions have higher regularity, the rate can be faster.

12 pages, 1 figure. v2:additional result in Theorem 1.3, typos corrected

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