= Solution
An <equilibrium point> $p=(x_0,y_0)$ of an <autonomous planar system> is a point where its <vector field> vanishes:
$$
\boxed{X(x_0,y_0)=Y(x_0,y_0)=0.}
$$
For a locally well-posed <ordinary differential equation>, <Lyapunov stability> means that every prescribed neighbourhood can be protected by choosing a sufficiently small initial neighbourhood. More precisely, for every $\varepsilon>0$ there exists $\delta>0$ such that every trajectory starting with $\|p(0)-p\|<\delta$ exists for all $t\geq0$ and satisfies
$$
\boxed{\|p(t)-p\|<\varepsilon\quad\text{for all }t\geq0.}
$$
The number $\delta$ may depend on $\varepsilon$ but not on the particular starting point. <Asymptotic stability> additionally requires convergence to the <equilibrium point> for all sufficiently close starting points.
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