Pointwise recurrent homeomorphisms with stable fixed points (Q818364)

A homeomorphism \(f: X\to X\) of a compact metric space \(X\) is called pointwise recurrent if \(x\in L^+(x)\cap L^-(x)\) for every \(x\in X\), where \(L^+(x)\) and \(L^-(x)\) are the positive and negative limit sets of \(x\), respectively. Among other important results the author proves that a pointwise recurrent, orientation preserving homeomorphism of the 2-sphere, which is different from the identity, and whose fixed points are stable in the sense of Lyapunov, must have exactly two fixed points.