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تسجيل مستخدم جديدClassical Morse theory revisited I -- Backward $lambda$-Lemma and homotopy type
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تأليف
Joa Weber
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We introduce two tools, dynamical thickening and flow selectors, to overcome the infamous discontinuity of the gradient flow endpoint map near non-degenerate critical points. More precisely, we interpret the stable fibrations of certain Conley pairs $(N,L)$, established in [2,3], as a dynamical thickening of the stable manifold. As a first application and to illustrate efficiency of the concept we reprove a fundamental theorem of classical Morse theory, Milnors homotopical cell attachment theorem [1]. Dynamical thickening leads to a conceptually simple and short proof.
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We reprove the $lambda$-Lemma for finite dimensional gradient flows by generalizing the well-known contraction method proof of the local (un)stable manifold theorem. This only relies on the forward Cauchy problem. We obtain a rather quantitative desc
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