Finding positively invariant sets of a class of nonlinear loops via curve fitting

In this paper, we study positively invariant sets of a class of nonlinear loops and discuss the relation between these sets and the attractors of the loops. For the canonical Hénon map, a numerical method based on curve fitting is proposed to find a positively invariant set containing the strange attractor. This work can be generalized to find inequality termination conditions for loops with nonlinear assignments.

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