Given a dynamical system $(X,G)$,
def1. A point $x\in X$ is called periodic, if there exist a syndetic set $S\subseteq G$, such that $Sx=\{x\}$.
def2. A point $x\in X$ is called periodic, if $Gx$ is a minimal and finite subset of $X$.
def3. A point $x\in X$ is called periodic, if $G/G_x$ is compact, where $G$ is a topological group and $G_x$ is the isotropy group of $x$.
Are these definition equivalent?
