@article{Weber_2016, title={Classical Morse theory revisited - I backward $\lambda$-lemma and homotopy type}, volume={47}, url={https://apcz.umk.pl/TMNA/article/view/TMNA.2016.020}, DOI={10.12775/TMNA.2016.020}, abstractNote={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 \cite{weber:2014c}, as a \emph{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, Milnor’s homotopical cell attachment theorem \cite{milnor:1963a}. Dynamical thickening leads to a conceptually simple and short proof.}, number={2}, journal={Topological Methods in Nonlinear Analysis}, author={Weber, Joa}, year={2016}, month={Jun.}, pages={641–646} }