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arXiv · 2112.14690

Regulated curves on a Banach manifold and singularities of endpoint map. I. Banach manifold structure

Tomasz Goliński·Fernand Pelletier
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Abstract

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.

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Tomasz Goliński, Fernand Pelletier. 2021-12-29. Regulated curves on a Banach manifold and singularities of endpoint map. I. Banach manifold structure. https://doi.org/10.1016/j.difgeo.2025.102245

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