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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Chaos in the Lorenz equations:
A computer assisted proof.
Part II: Details


Authors: Konstantin Mischaikow and Marian Mrozek
Journal: Math. Comp. 67 (1998), 1023-1046
MSC (1991): Primary 58F13, 54H20, 65L99, 34-04, 68T15
MathSciNet review: 1459392
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Abstract | References | Similar Articles | Additional Information

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
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

DOI: http://dx.doi.org/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.
Article copyright: © Copyright 1998 American Mathematical Society