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 comp lex plane. Using this property, we present two methods for constructin g sequences of functions, which may be explicitly computed from the sy stem, and from which one can deduce whether a specific point belongs t o the attractor or not. Approximation methods obtained in this way are tested on the Lorenz system and compared with those from Foias and Jo lly (1995 Nonlinearity 8 295-319).