homoclinic

If $X$ is a topological space and $f$ is a flow on $X$ or an homeomorphism mapping $X$ to itself, we say that $x\in X$ is an homoclinic point (or homoclinic intersection) if it belongs to both the stable and unstable sets of some fixed or periodic point $p$; i.e.

$$x\in W^s(f,p)\cap W^u(f,p).$$

The orbit of an homoclinic point is called an homoclinic orbit.