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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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Chaos in the Lorenz equations: A computer assisted proof. Part II: Details
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by Konstantin Mischaikow and Marian Mrozek PDF
Math. Comp. 67 (1998), 1023-1046 Request permission

Abstract:

Details of a new technique for obtaining rigorous results concerning the global dynamics of nonlinear systems is described. The technique combines abstract existence results based on the Conley index theory with rigorous computer assisted computations. As an application of these methods it is proven that for some explicit parameter values the Lorenz equations exhibit chaotic dynamics.
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Additional Information
  • Konstantin Mischaikow
  • Affiliation: Center for Dynamical Systems and Nonlinear Studies School of Mathematics Georgia Institute of Technology Atlanta, Georgia 30332-0001
  • MR Author ID: 249919
  • Email: mischaik@math.gatech.edu
  • Marian Mrozek
  • Affiliation: Center for Dynamical Systems and Nonlinear Studies School of Mathematics Georgia Institute of Technology Atlanta, Georgia 30332-0001
  • Address at time of publication: Instytut Informatyki, Uniwersytet Jagielloński, Kraków, Poland
  • Email: mrozek@ii.uj.edu.pl
  • Received by editor(s): August 11, 1995
  • Received by editor(s) in revised form: April 12, 1996, and February 18, 1997
  • Additional Notes: Research of the first author was supported in part by NSF grant 9302970.
    Research of the second author was supported by KBN, Grant 0449/P3/94/06.
  • © Copyright 1998 American Mathematical Society
  • Journal: Math. Comp. 67 (1998), 1023-1046
  • MSC (1991): Primary 58F13, 54H20, 65L99, 34-04, 68T15
  • DOI: https://doi.org/10.1090/S0025-5718-98-00945-4
  • MathSciNet review: 1459392