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

Authors:
Liyong Shen;Min Wu;Zhengfeng Yang;Zhenbing Zeng
Affiliations:
Graduate University of CAS, Beijing, China;East China Normal University, Shanghai, China;East China Normal University, Shanghai, China;East China Normal University, Shanghai, China
Venue:
Proceedings of the 2009 conference on Symbolic numeric computation
Year:
2009

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Abstract

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.