Almost all books on differential equations discuss fixed points where the flow vanishes, i.e., for a system of the following kind $$ \dot{\mathbf{x}} = f(\mathbf{x}) $$ points $\mathbf{x}$ where $f(\mathbf{x}) = 0$.
However, much of the discussion revolves around isolated fixed points. But there can also be cases where the flow vanishes along a manifold, e.g., for the Hamiltonian system with the Hamiltonian $H = p^2x$, we have $$ \begin{align} \dot{x} = \partial_{p}H &= 2px\\ \dot{p} = -\partial_{x}H &= -p^2 \end{align} $$ and the flow vanishes on the $x$ axis since $p = 0$ there. (Strogatz discusses a very similar example in Problem 6.5.12 of his book on nonlinear dynamics.) Is there a specific way of referring to this sort of "fixed manifolds" (for lack of a better word)? Are there any generally applicable results for such non-isolated fixed points?