How to define periodicity of orbits for general group actions?

Question

Let $H$ be a topological group acting on a topological space $X$. Is there a general definition of periodicity in this case? Write $X=G/\Gamma$ and consider the orbit $Hg\Gamma$, what does it mean for the orbit $Hg\Gamma$ to be periodic? If there is an abstract definition, I also wish to know the intuition behind it.

Answer 1

The following is taken from Wikipedia:

For a general dynamical system, especially in homogeneous dynamics, when one has a "nice" group $G$ acting on a probability space $X$ in a measure-preserving way, an orbit $G.x \subset X$ will be called periodic (or equivalently, closed) if the stabilizer $\text{Stab}_{G}(x)$ is a lattice inside $G$.