Mathematics of Computation

Author(s): Konstantin Mischaikow; Marian Mrozek.
Journal: Math. Comp. 67 (1998), 1023-1046.
MSC (1991): Primary 58F13, 54H20, 65L99, 34-04, 68T15
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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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Konstantin Mischaikow
Affiliation: Center for Dynamical Systems and Nonlinear Studies School of Mathematics Georgia Institute of Technology Atlanta, Georgia 30332-0001
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 Jagiellonski, Kraków, Poland
Email: mrozek@ii.uj.edu.pl

DOI: 10.1090/S0025-5718-98-00945-4
PII: S 0025-5718(98)00945-4
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 of article: Copyright 1998, American Mathematical Society

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