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arXiv · 2107.12175

The regularized free fall II -- Homology computation via heat flow

Urs Frauenfelder·Joa Weber
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Abstract

In [BOV20] Barutello, Ortega, and Verzini introduced a non-local functional which regularizes the free fall. This functional has a critical point at infinity and therefore does not satisfy the Palais-Smale condition. In this article we study the $L^2$ gradient flow which gives rise to a non-local heat flow. We construct a rich cascade Morse complex which has one generator in each degree $k\ge 1$. Calculation reveals a rather poor Morse homology having just one generator. In particular, there must be a wealth of solutions of the heat flow equation. These can be interpreted as solutions of the Schrödinger equation after a Wick rotation.

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Urs Frauenfelder, Joa Weber. 2021-07-22. The regularized free fall II -- Homology computation via heat flow. https://doi.org/10.12775/tmna.2021.060

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