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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2404.07614 |
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| _version_ | 1866909488764682240 |
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| author | Caponio, Erasmo Masiello, Antonio Suhr, Stefan |
| author_facet | Caponio, Erasmo Masiello, Antonio Suhr, Stefan |
| contents | We consider a differential inclusion on a manifold, defined by a field of open half-spaces whose boundary in each tangent space is the kernel of a one-form. We make the assumption that the corank one distribution associated to the kernel is completely nonholonomic of step 2. We identify a subset of solutions of the differential inclusion, satisfying two endpoints and periodic boundary conditions, which are homotopy equivalent in the $W^{1,p}$-topology, for any $p\in [1,+\infty)$, to the based loop space and the free loop space respectively. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07614 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On homotopy properties of solutions of some differential inclusions in the $W^{1,p}$-topology Caponio, Erasmo Masiello, Antonio Suhr, Stefan Dynamical Systems Differential Geometry 34A60, 58B05, 93C10 We consider a differential inclusion on a manifold, defined by a field of open half-spaces whose boundary in each tangent space is the kernel of a one-form. We make the assumption that the corank one distribution associated to the kernel is completely nonholonomic of step 2. We identify a subset of solutions of the differential inclusion, satisfying two endpoints and periodic boundary conditions, which are homotopy equivalent in the $W^{1,p}$-topology, for any $p\in [1,+\infty)$, to the based loop space and the free loop space respectively. |
| title | On homotopy properties of solutions of some differential inclusions in the $W^{1,p}$-topology |
| topic | Dynamical Systems Differential Geometry 34A60, 58B05, 93C10 |
| url | https://arxiv.org/abs/2404.07614 |