We refer to the collection of initial conditions whose
orbits result in a particular behavior as the * basin* of that
particular type of behavior. (This is a slight generalization of the
concept of a * basin of attraction* to which it reduces if we
identify the ``behaviors'' as motions on attractors.) A point p is a
* boundary point* of a basin B if every open neighborhood
of p intersects the basin B and at least one other basin. The
set of all boundary points for a particular basin is
the * boundary* of that basin. The basin boundary is termed
* fractal* [Grebogi * et al.*, 1983a, 1983b; Takesue & Kaneko, 1984;
MacDonald * et al.*, 1985; Moon & Li, 1985; Gwinn & Westervelt, 1986]
when its box-counting dimension is not integral. In general, this
implies the existence of an unstable chaotic invariant
set embedded in the fractal basin boundary [Grebogi * et al.*,
1986, 1987b, 1987c, 1988].

The term * Wada property* was used by Kennedy and Yorke [1991]
to describe sets which have certain interesting topological features.
Specifically, a boundary point p is called a * Wada point* if every
open neighborhood of p intersects at least three different basins. A
basin boundary has this Wada property when every boundary point of the basin is
a Wada point. The boundary for such a basin is called a * Wada basin
boundary*.

The system we have elected to study to show this Wada property is a simple
two-dimensional billiard problem that has been extensively studied
[Eckhardt, 1987; Gaspard & Rice, 1989a, 1989b, 1989c; Gaspard & Ramirez, 1992]
and serves as a nice paradigm model of chaotic
scattering. The system consists of three circular hard disks, each of radius
R. The centers of these disks are located on the vertices of an equilateral
triangle whose side length is L > 2R, as shown in Fig. 1. For
convenience, the origin of the coordinate system is chosen such that it
coincides with the center of the leftmost disk. Particles move in straight
lines between perfectly elastic collisions with the disks. The angle of
incidence equals the angle of reflection at each collision. (Note that
as shown in the inset to
Fig. 1, the three disk problem is also relevant as a simple
model of a mesoscopic junction, where the three leads correspond to three
exit modes of electrons in the scattering region [Jalabert * et al.*, 1990].)