and when time is not continuous but assumes only discrete values by difference equations (maps):

For dissipative systems, phase-space volumes are contracted by the time evolution. The trajectory (orbit) of such a system typically settles on a subset of , called an attractor [Eckmann and Ruelle, 1985]. For example, the attractor of a damped pendulum is a fixed point, while the attractor of a periodically forced pendulum is a limit cycle. On a strange attractor, trajectories wander in an apparently erratic manner and they are highly sensitive to initial conditions. For a zoo of strange attractors, see Ref. [Holden and Muhamad, 1986].

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