Topology of attractors and periodic points Ortega Ríos, Rafael Ruiz Herrera, Alfonso The dynamics of a dissipative and area contracting planar homeomorphism were described in terms of the attractor. This was a subset of the plane defined as the maximal compact invariant set. We proved that the coexistence of two fixed points and an N-cycle produced some topological complexity: the attractor cannot be arcwise connected. The proofs were based on the theory of prime ends. 2024-10-23T11:16:40Z 2024-10-23T11:16:40Z 2024-10 journal article Ortega Río,s R. & Ruíz Herrera, A. [doi:10.3934/cpaa.2024083] https://hdl.handle.net/10481/96282 10.3934/cpaa.2024083 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional American Institute of Mathematical Sciences (AIMS)