Ortega, RefaelRomero Ruiz del Portal, Francisco2023-06-202023-06-2020111435-985510.4171/JEMS/288https://hdl.handle.net/20.500.14352/42534Given an orientation-preserving homeomorphism of the plane, a rotation number can be associated with each locally attracting fixed point. Assuming that the homeomorphism is dissipative and the rotation number vanishes we prove the existence of a second fixed point. The main tools in the proof are Caratheodory prime ends and fixed point index. The result is applicable to some concrete problems in the theory of periodic differential equations.engjournal articlehttp://www.ems-ph.org/journals/show_pdf.php?issn=1435-9855&vol=13&iss=6&rank=2open access517.9Planar attractorPrime endFixed point indexGlobal asymptotic stabilityInvariant rayPeriodic differential equationExtinctionEcuaciones diferenciales1202.07 Ecuaciones en Diferencias