  One of the common characteristics of chaotic maps or flows in high dimensions
is "unstable dimensional variability", in which there are periodic points whose
unstable manifolds have different dimensions. In this paper, in trying to
characterize such systems we define a property called "multi-chaos". A set $X$
is multi-chaotic if $X$ has a dense trajectory and for at least 2 values of
$k$, the $k$-dimensionally unstable periodic points are dense in $X$. All
proofs that such a behavior holds have been based on hyperbolicity in the sense
that (i) there is a chaotic set $X$ with a dense trajectory and (ii) in X there
are two or more hyperbolic sets with different unstable dimensions. We present
a simple 2-dimensional paradigm for multi-chaos in which a quasiperiodic orbit
plays the key role, replacing the large hyperbolic set.
