Dynamical Morse entropy
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866909228187254784 |
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| author | Bertelson, Mélanie Gromov, Misha |
| author_facet | Bertelson, Mélanie Gromov, Misha |
| contents | We consider actions of a tileable amenable group $Γ$ 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 $Γ$. 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_14410 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamical Morse entropy Bertelson, Mélanie Gromov, Misha Dynamical Systems Differential Geometry 37B40, 54C70 We consider actions of a tileable amenable group $Γ$ 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 $Γ$. 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. |
| title | Dynamical Morse entropy |
| topic | Dynamical Systems Differential Geometry 37B40, 54C70 |
| url | https://arxiv.org/abs/2406.14410 |