For a number of years, different authors were using different definitions of "chaos", but I think that has settled down now.
"Quantum group" may be a good answer. If Wikipedia can be trusted on this issue, "In mathematics and theoretical physics, the term quantum group denotes various kinds of noncommutative algebra with additional structure. In general, a quantum group is some kind of Hopf algebra. There is no single, all-encompassing definition, but instead a family of broadly similar objects."