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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Computational unsolvability of domains of attraction of nonlinear systems
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by Ning Zhong PDF
Proc. Amer. Math. Soc. 137 (2009), 2773-2783 Request permission

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.
References
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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
  • 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
  • © Copyright 2009 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 137 (2009), 2773-2783
  • MSC (2000): Primary 03D80; Secondary 34D45, 68Q17
  • DOI: https://doi.org/10.1090/S0002-9939-09-09851-7
  • MathSciNet review: 2497492