The convexity of closed orbits of Liénard systems (Q1943228)

Consider the planar system \[ {dx\over dt}= F(x)- y,\quad\frac{dy}{dt}= x\tag{\(*\)} \] under the condition that \(F\in C^2(\mathbb R,\mathbb R)\) and satisfies \[ F(0)= 0\text{ and } F''(x)\neq 0\text{ for }x\in G:= \{x\in\mathbb{R}\setminus\{0\}: |F'(x)|\geq 2\}. \] In this situation, the authors prove that any closed orbit of \((*)\) is strictly convex.