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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Computational unsolvability of domains of attraction of nonlinear systems


Author: Ning Zhong
Journal: Proc. Amer. Math. Soc. 137 (2009), 2773-2783
MSC (2000): Primary 03D80; Secondary 34D45, 68Q17
Published electronically: February 3, 2009
MathSciNet review: 2497492
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Abstract: Let $ S$ be the domain of attraction of a computable and asymptotically stable hyperbolic equilibrium point of the non-linear system $ \dot{x}=f(x)$. We show that the problem of determining $ S$ is computationally unsolvable. We also present an upper bound of the degree of unsolvability of this problem.


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Additional Information

Ning Zhong
Affiliation: Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Ohio 45221-0025
Email: Ning.Zhong@uc.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09851-7
PII: S 0002-9939(09)09851-7
Keywords: Recursive open/closed subsets of $\mathbb {R}^n$, r.e. open/closed subsets of $\mathbb {R}^n$, computable functions, continuous dynamical systems, domain of attraction of an asymptotically stable equilibrium point.
Received by editor(s): July 11, 2008
Received by editor(s) in revised form: December 8, 2008
Published electronically: February 3, 2009
Communicated by: Julia Knight
Article copyright: © Copyright 2009 American Mathematical Society