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Pestered by many (in my opinion, fundamental) questions and no literature at hand to answer them, I resort to posing my questions here. Let me start with the following. (Hopefully I have the correct subsection.)

I am inspecting a dynamical, autonomous and conservative system driven by a 'conservative' vector-field:

[tex]\left\|\dot{\mathbf{x}}\right\|_1 = 0[/tex]

(No need to specify this any further).

If we start off with

[tex]\left\|\mathbf{x}\right\|_1 = n[/tex]

Then the system we inspect is a vector-field on ann-simplex.

To be honest I am in doubt about this being a proper manifold, since the tangent has to abide the conservation constraints, while the neighborhood of any point in the state space is not perfectly Euclidean.

In line with this: how accurate is a Taylor-expansion of a subspace cut off at them-th term?

Any response would be very much appreciated!

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# Conservative vector field; classification of derivative

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