Here is the full construction of the example:

* Manifold \$$M\$$ = unit disc
* Trajectory \$$\phi^x(t) = x\ /\ t\$$

Clearly all paths converge to the origin, which is the unique attractor point.

In the discrete case, \$$T\$$ is the natural numbers, and we have a semi-cascade.

In the continuous case, \$$T\$$ is the non-negative real numbers, and we have a semi-flow.