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Universität Augsburg
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Universität Augsburg
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Joa Weber
Campinas
spricht am
Montag, 21. Dezember 2015
um
16:00 Uhr
im
Raum 2004 (L1)
über das Thema:
| Abstract: |
| Consider the (forward) heat (semi-)flow on the loop space of a closed Riemannian manifold. We review a construction of invariant foliations near a hyperbolic fixed point parametrized by the local unstable manifold, the center leaf being the local stable manifold. One can think of the collection of leaves as a topological thickening of the local stable manifold. It is useful to equip each leaf, via conjugation, with a copy of the flow on the local stable manifold. The advantage is that such 'dynamical thickening' removes the notorious discontinuity of the trajectory endpoint map. As a first application we illustrate this in the finite dimensional case of a downward gradient flow of a Morse function by indicating an alternative proof of the classical cell attachment theorem in Morse theory. Another (potential) application is to extend towards parabolic PDEs Rot-Vandervorst's recent Conley homology theory [arXiv:1305.4074] which lives in finite dimensions and is based on the construction of Morse homology via hyperbolic dynamical systems (lambda-lemma and Grobman- Hartman theorem). |
| Hierzu ergeht herzliche Einladung. |
Kaffee, Tee und Gebäck eine halbe Stunde vor Vortragsbeginn im Raum 2006 (L1).