Discovery of closed orbits of dynamical systems with the use of computers
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In this paper we derive a general criterion which can be used for the discovery with the use of a computer of closed orbits of systems of ordinary differential equations. We apply this criterion to the Lorenz model and show rigorously the existence of a closed orbit for the case under consideration. In a subsequent paper we shall show how the stable manifold of this orbit determines the boundary of the stochastic attractor.
Key wordsPoincaré mapping linear system of equations in variations closed orbit attractor
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