Chaos in the Lorenz equations: a computer-assisted proof-Reference-Cited by-同舟云学术

Chaos in the Lorenz equations: a computer-assisted proof

Published:1995 Issue:1 Volume:32 Page:66-72
ISSN:0273-0979
Container-title:Bulletin of the American Mathematical Society
language:en
Short-container-title:Bull. Amer. Math. Soc.

Author:

Mischaikow Konstantin,Mrozek Marian

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/bull/1995-32-01/S0273-0979-1995-00558-6/S0273-0979-1995-00558-6.pdf

Reference8 articles.

1. A shooting approach to the Lorenz equations;Hastings, S. P.;Bull. Amer. Math. Soc. (N.S.),1992

2. Conley index for discrete multi-valued dynamical systems;Kaczynski, T.;Topology Appl.,1995

3. Isolating neighborhoods and chaos;Mischaikow, Konstantin;Japan J. Indust. Appl. Math.,1995

4. K. Mischaikow and M. Mrozek, Chaos in Lorenz equations: A computer assisted proof, Part II: Details, in preparation.

5. Leray functor and cohomological Conley index for discrete dynamical systems;Mrozek, Marian;Trans. Amer. Math. Soc.,1990

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