Localization of attractors by their analytic properties

The global attractor of a dissipative system of ordinary differential equations can be characterized as the set of solutions which permit an extension to a bounded analytic function on a uniform strip in a complex plane. Using this property, we present two methods for constructing sequences of functions, which may be explicitly computed from the system, and from which one can deduce whether a specific point belongs to the attractor or not. Approximation methods obtained in this way are tested on the Lorenz system and compared with those from Foias and Jolly (1995 Nonlinearity 8 295-319).