On the flows of linear vector fields

M. Jotz

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arXiv · 2409.18723

On the flows of linear vector fields

M. Jotz

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Abstract

This note provides a detailed proof of the fact that a linear vector field on a vector bundle has a flow by vector bundle isomorphisms. It then implies easily the existence of global solutions to linear non-autonomous ODE's, with a standard time-dependent flow construction. As a further application, a simple proof of the smooth triviality of vector bundles over contractible bases is given. Finally, a detailed elementary proof of the isomorphy (as Lie algebras) of all fibers of the kernel of a transitive Lie algebroid is given.

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M. Jotz. 2024-09-27. On the flows of linear vector fields. https://arxiv.org/abs/2409.18723

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