Dynamical system is generated by:
$x'=-x+f(x,y)$
$y'=-y+g(x,y)$
$f,g \in C^1$ and $f,g$ are bounded.
Prove that the omega limit set of p: $\omega(p) \neq \emptyset$ for all $p \in \mathbb{R}^2$.
I can say that if $f_{y}g_{x} \in (0,1)$ Jacobian \begin{pmatrix}-1&f_{y}\\g_{x}&-1\\ \end{pmatrix} has negative eigenvalues, and $\omega(p) = (0,0)$ for all $p \in \mathbb{R}^2$. But it's not much...