Given a continuous group action $G \times X \rightarrow X$ on a topological space $X$, is there a standard term for the subsets $K \subset X$ for which
- Every open neighborhood of $K$ intersects every group orbit;
- $K$ is minimal with respect to the previous property ?
Examples: points of $X$ if the action is transitive or ergodic, a meridian in $S^2$ if the action is rotating the sphere around the poles, the limit cycle plus the fixed point in the Van der Pol oscillator.
Edit. Maybe "minimality" is not the right term. In the examples above, you can replace the meridian for a dense set of points on the meridian and the same with the limit cycle in the Van der Pol oscillator (i.e., the examples are not really examples or, rather, they are examples of the phenomenon I wish to describe, but have failed to do).
