Rigorous Models for the Lorenz Equations
نویسنده
چکیده
Inspired by numerical solutions of the Lorenz equations, we model the Poincar e map of the ow by a one-parameter map of the unit interval. For a certain region in the parameter space of the Lorenz equations, we show that the corresponding one-dimensional map is chaotic, imposing only minimal conditions on its derivative. Perturbing the map, we get a two-dimensional map corresponding to a ow in three dimensions. We show that the chaotic property is preserved under certain perturbations.
منابع مشابه
Chaos in the Lorenz equations: A computer assisted proof. Part II: Details
Details of 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 rigorous computer assisted computations. As an application of these methods it is proven that for some explicit parameter values the Lorenz equations exhibit chaotic dynamics.
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