An average intersection estimate for families of diffeomorphisms
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866917622155575296 |
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| author | Kodat, Axel Shub, Michael |
| author_facet | Kodat, Axel Shub, Michael |
| contents | We show that for any sufficiently rich compact family $\mathcal{H}$ of $C^1$ diffeomorphisms of a closed Riemannanian manifold $M$, the average geometric intersection number over $h \in \mathcal{H}$ between $h(V)$ and $W$, for $V, W$ any complementary dimensional submanifolds of $M$, is approximately (i.e. up to a uniform multiplicative error depending only on $\mathcal{H}$) the product of their volumes. We also give a construction showing that such families always exist. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_17349 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | An average intersection estimate for families of diffeomorphisms Kodat, Axel Shub, Michael Differential Geometry Dynamical Systems We show that for any sufficiently rich compact family $\mathcal{H}$ of $C^1$ diffeomorphisms of a closed Riemannanian manifold $M$, the average geometric intersection number over $h \in \mathcal{H}$ between $h(V)$ and $W$, for $V, W$ any complementary dimensional submanifolds of $M$, is approximately (i.e. up to a uniform multiplicative error depending only on $\mathcal{H}$) the product of their volumes. We also give a construction showing that such families always exist. |
| title | An average intersection estimate for families of diffeomorphisms |
| topic | Differential Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2403.17349 |