Attractor
Dynamical systems
A set of states that is invariant under the dynamics, attracts all nearby starting states over time, and contains no proper subset with both properties.
What is usually left out
All three conditions are needed. Without invariance the set is not preserved by the dynamics; without attracting a whole neighbourhood, a single unstable point would qualify; without minimality, any set containing a genuine attractor would qualify too, including the entire state space.