title: Stability and attractivity in discrete dynamical systems.
abstract: It is proven that one-dimensional discrete dynamical systems do not possess attractors that are unstable. Also, a C1 two-dimensional discrete system with a global attractor that is unstable is constructed.
authors.affiliation: Mathematics Department, California State University, Fullerton 92634, USA.
authors.forename: M
authors.initials: M
authors.lastname: Martelli
authors.forename: D
authors.initials: D
authors.lastname: Marshall
mesh_terms: D008962:Models, Theoretical; D017711:Nonlinear Dynamics