ATRACTOR

Let \[\begin{array}{rl} f:\left[-\frac{5}{2},\frac{5}{2}\right] & \rightarrow\mathbb{R}^{2}\\ t & \rightarrow\left(t^{3}-4,\, t^{2}-4\right) \end{array}\]

Then \(f'(t)=\left(3t^{2}-4,\,2t\right)\); \(v(t)=\left|f'(t)\right|=\sqrt{16-20t^{2}+9t^{4}}\) and the trace of this curve is:

Observe that \(f(2)=f(-2)=(0,0)\), which implies that the function is not injective. This means that the particle will be in point \((0,0)\) in two different moments.