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Chaos in the Lorenz Equations: a Computer-Assisted Proof
Author(s):
Konstantin
Mischaikow;
Marion
Mrozek
Journal:
Bull. Amer. Math. Soc.
32
(1995),
66-72.
MSC (1991):
Primary 58F13
MathSciNet review:
1276767
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Additional information
References:
- [1]
- S. P. Hastings and W. C. Troy, A shooting approach to the Lorenz equations, Bull. Amer. Math. Soc. (N.S.) \textbf{27} (1992), 298--303. MR 1161275
- [2]
- T. Kaczy\'{n}ski and M. Mrozek, Conley index for discrete multivalued dynamical systems, Topology Appl.
- [3]
- K. Mischaikow and M. Mrozek, Isolating neighborhoods and chaos, preprint. MR 1337206
- [4]
- K. Mischaikow and M. Mrozek, Chaos in Lorenz equations\,{\rm :} A computer assisted proof, Part {\rm II:} Details, in preparation.
- [5]
- M. Mrozek, Leray functor and the cohomological Conley index for discrete dynamical systems, Trans. Amer. Math. Soc. \textbf{318} (1990), 149--178. MR 968888
- [6]
- M. Mrozek, Topological invariants, multivalued maps and computer assisted proofs in dynamics, in preparation.
- [7]
- M. R. Rychlik, Lorenz attractors through \v {S}il`nikov-type bifurcation. Part {\rm I}, Ergodic Theory Dynamical Systems \textbf{10} (1989), 793--821. MR 1091428
- [8]
- B. Hassard, S. P. Hastings, W. C. Troy, and J. Zhang, A computer proof that the Lorenz equations have {\rm ``}chaotic{\rm ''} solutions, Appl. Math. Lett. \textbf{7} (1994), 79--83. MR 1349899
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Additional Information:
DOI:
10.1090/S0273-0979-1995-00558-6
PII:
S 0273-0979(1995)00558-6
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