Chaos in the lorenz equations: A computer-assisted proof

Konstantin Mischaikow; Marian Mrozek

doi:10.1090/S0273-0979-1995-00558-6

Chaos in the lorenz equations: A computer-assisted proof

Konstantin Mischaikow, Marian Mrozek

Research output: Contribution to journal › Comment/debate › peer-review

169 Scopus citations

Abstract

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 computer-assisted computations. As an application of these methods it is proven that for an explicit parameter value the Lorenz equations exhibit chaotic dynamics.

Original language	English (US)
Pages (from-to)	66-72
Number of pages	7
Journal	Bulletin of the American Mathematical Society
Volume	32
Issue number	1
DOIs	https://doi.org/10.1090/S0273-0979-1995-00558-6
State	Published - Jan 1995
Externally published	Yes

All Science Journal Classification (ASJC) codes

Mathematics(all)
Applied Mathematics

Access to Document

10.1090/S0273-0979-1995-00558-6

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title = "Chaos in the lorenz equations: A computer-assisted proof",

abstract = "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 computer-assisted computations. As an application of these methods it is proven that for an explicit parameter value the Lorenz equations exhibit chaotic dynamics.",

author = "Konstantin Mischaikow and Marian Mrozek",

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