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| Natura: | Preprint |
| Pubblicazione: |
2021
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| Accesso online: | https://arxiv.org/abs/2112.14690 |
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| _version_ | 1866913775657943040 |
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| author | Goliński, Tomasz Pelletier, Fernand |
| author_facet | Goliński, Tomasz Pelletier, Fernand |
| contents | We consider regulated curves in a Banach bundle whose projection on the basis is continuous with regulated derivative. We build a Banach manifold structure on the set of such curves. This result was previously obtained for the case of strong Riemannian Banach manifold and absolutely continuous curves in arXiv:1612.02604. The essential argument used was the existence of a "local addition" on such a manifold. Our proof is true for any Banach manifold. In the second part of the paper the problems of controllability will be discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2112_14690 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Regulated curves on a Banach manifold and singularities of endpoint map. I. Banach manifold structure Goliński, Tomasz Pelletier, Fernand Functional Analysis Differential Geometry 53A04, 46T10, 46B99 We consider regulated curves in a Banach bundle whose projection on the basis is continuous with regulated derivative. We build a Banach manifold structure on the set of such curves. This result was previously obtained for the case of strong Riemannian Banach manifold and absolutely continuous curves in arXiv:1612.02604. The essential argument used was the existence of a "local addition" on such a manifold. Our proof is true for any Banach manifold. In the second part of the paper the problems of controllability will be discussed. |
| title | Regulated curves on a Banach manifold and singularities of endpoint map. I. Banach manifold structure |
| topic | Functional Analysis Differential Geometry 53A04, 46T10, 46B99 |
| url | https://arxiv.org/abs/2112.14690 |