But now let's look at how ODEs _can_ be used to define flows. There are two links in the chain here:

1. The ODEs specify a field of tangent vectors on the manifold.
2. A tangent vector field determines a flow.

For information about (2), see:

* [Flow of a vector field](https://ncatlab.org/nlab/show/flow+of+a+vector+field), nLab.