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The Laplace-Beltrami eigenfunctions on a compact Riemannian manifold $M$whose geodesic billiard flow has mixed character have been conjectured byPercival to split into two complementary families, with all semiclassical masssupported in the completely integrable and ergodic regions of phase spacerespectively. In this paper, we consider the Dirichlet Laplacian on a family ofmushroom billiards $M_t$ parametrised by the length $t\in(0,2]$ of theirrectangular part. We prove that $M_t$ satisfies Percival's conjecture foralmost all $t\in(0,2]$, hence providing the first example of a billiard knownto satisfy Percival's conjecture.

Percival's Conjecture for the Bunimovich Mushroom Billiard