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Chaos in the Lorenz equations: a computer-assisted proof
Author(s):
Konstantin
Mischaikow;
Marian
Mrozek
Journal:
Bull. Amer. Math. Soc.
32
(1995),
66-72.
MathSciNet review:
1276767
Retrieve article in:
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Abstract |
References |
Additional information
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.
References:
-
- [1]
- S. P. Hastings and W. C. Troy, A shooting approach to the Lorenz equations, Bull. Amer. Math. Soc. (N.S.) 27 (1992), 298-303. MR 1161275 (93f:58150)
- [2]
- T. Kaczynński and M. Mrozek, Conley index for discrete multivalued dynamical systems, Topology Appl. (to appear). MR 1354383 (97d:54066)
- [3]
- K. Mischaikow and M. Mrozek, Isolating neighborhoods and chaos, preprint. MR 1337206 (96e:58104)
- [4]
- -, Chaos in Lorenz equations: A computer assisted proof, Part II: Details, in preparation.
- [5]
- M. Mrozek, Leray functor and the cohomological Conley index for discrete dynamical systems, Trans. Amer. Math. Soc. 318 (1990), 149-178. MR 968888 (90f:34076)
- [6]
- -, Topological invariants, multivalued maps and computer assisted proofs in dynamics, in preparation.
- [7]
- M. R. Rychlik, Lorenz attractors through Šil'nikov-type bifurcation. Part I, Ergodic Theory Dynamical Systems 10 (1989), 793-821. MR 1091428 (92f:58103)
- [8]
- B. Hassard, S. P. Hastings, W. C. Troy, and J. Zhang, A computer proof that the Lorenz equations have "chaotic" solutions, Appl. Math. Lett. 7 (1994), 79-83. MR 1349899 (96d:58082)
Additional Information:
DOI:
10.1090/S0273-0979-1995-00558-6
PII:
S 0273-0979(1995)00558-6
Copyright of article:
Copyright
1995,
American Mathematical Society
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