We study experimentally and numerically properties of quarter-stadium billiard's eigenfunctions in the regime of quantum cantori. A quarter-stadium billiard was simulated experimentally by a thin quarter-stadium microwave cavity. Experimental eigenfunctions in the cantori regime N=7--63 of the quarter-stadium microwave billiard with the parameter \varepsilon =0.1 were reconstructed using a field perturbation technique and a circular wave expansion method. The eigenfunctions N=76--499 lying in the cantori regime of the quarter-stadium billiard with \varepsilon =0.05 were investigated numerically.

PACS numbers: 05.45.Mt