33 research outputs found
Mixing in an anharmonic potential well
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 . 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.Comment: 12 pages, 1 figure. v2:additional result in Theorem 1.3, typos
correcte