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arXiv · 2406.14410

Dynamical Morse entropy

Mélanie Bertelson·Misha Gromov
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Abstract

We consider actions of a tileable amenable group $\Gamma$ on a topological space $X$. For a continuous function on $X$, we define the entropy of the number of homologically detectable critical point of the average of that function over $\Gamma$. This number is bounded below by the sum of the Betti number entropy. This result is thus a generalization of a standard Morse inequality in differential geometry to this setting.

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Mélanie Bertelson, Misha Gromov. 2024-06-20. Dynamical Morse entropy. https://arxiv.org/abs/2406.14410

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