Topology of attractors and periodic points

This is the authors' abstract. We don't add key points for this paper.

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.