Orbits and Phase Portraits in Dynamics
Definition 1
$$ O \left( x_{0} \right) := \left\{ x \in X : x = \varphi^{t} x_{0} , \forall t \in T \right\} $$ In the dynamical system given by $\left( T, X, \varphi^{t} \right)$, let’s denote the orbit of $x_{0} \in X$ as shown above. The partition of $X$ consisting of orbits is called the Phase Portrait of the dynamical system.
Kuznetsov. (1998). Elements of Applied Bifurcation Theory(2nd Edition): p8~10. ↩︎