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The interaction between topology and dynamical systems will be considered through shape theory tools. Namely, using the intrinsic approach to shape, the notion of proximate net will be introduced as a sequence of near continuous functions which converge in homotopical sense and a natural way of producing one in a given flow will be discussed. The central part of the presentation will be to generalize the shape-attractor theorem for Morse decomposition and to give the strong shape version, using the intrinsic approach. |
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