Ok, now let's head back towards the concrete.

Here's a recap of where we've gotten to.

* A flow defines a dynamical system

* ODEs define a tangent vector field

* We've just given a _definition_ of the concept of a global flow for a tangent vector field

But given the vector field defined by our ODEs, how do we know that there exists a some well-defined global flow for it?

Once we are assured of its existence, we can take that flow to be the dynamical system for the ODEs.

Here's a recap of where we've gotten to.

* A flow defines a dynamical system

* ODEs define a tangent vector field

* We've just given a _definition_ of the concept of a global flow for a tangent vector field

But given the vector field defined by our ODEs, how do we know that there exists a some well-defined global flow for it?

Once we are assured of its existence, we can take that flow to be the dynamical system for the ODEs.