Weak attractors from Lyapunov functions (Q5925881)

For a dynamical system \(f\) on a noncompact phase space \(X\), there appear various notions of attractors including the notions of a strong attractor and weak attractor. NEWLINENEWLINENEWLINELet \(X\) be a metric space that is both locally compact and \(\sigma\)-compact. Let \(A\) be a closed, nonempty, and \(f\)-invariant subset of \(X\). The author shows that if \(A\) is the zero set of a Lyapunov-type function on \(X\), then \(A\) is a weak attractor of \(f\).