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.References
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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