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The Lorenz attractor exists. (English. Abridged French version) Zbl 0935.34050

Summary: The author proves that the Lorenz equations support a strange attractor, as conjectured by E. Lorenz in 1963. It is proved that the attractor is robust, i.e., it persists under small perturbations of the coefficients in the underlying differential equations. The proof is based on a combination of normal form theory and rigorous numerical computations.

MSC:

34D45 Attractors of solutions to ordinary differential equations
34C28 Complex behavior and chaotic systems of ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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