Analytical Description of the Basin and the Transients of a Point Attractor of the Henon Mapping

摘要

Explicit expressions for closed curves C/sub n/ about the attractor that enclose a part of its basin are obtained. If n -> infinity the interior of C/sub n/ covers the complete basin. A sequence of invertible polynomial transformations is given, that converges rapidly towards the normal transformation, that transforms the nonlinear motion in the basin to a linear one. Using these transformations we obtain some practical tools to describe one aspect of the transient behavior in the basin. (ERA citation 10:050483)