📂Dynamics

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.