Attractors with vanishing rotation number (Q645350)

This paper analyses properties of point attractors with zero rotation number for orientation-preserving homeomorphism of the plane. Assuming that the homeomorphism is dissipative, the authors show that the existence of an asymptotically stable fixed point with zero rotation number implies the existence of a second fixed point. The proof exploits Carathéodory's theory of prime ends. Some applications are presented, relevant to population dynamics and the theory of nonlinear oscillations.