- #1

geoduck

- 257

- 2

If dσ/dt=X(σ)

for vector field X, then how does one interpret the solution:

σ(t)=exp[tX]σ(0) ?

If X is nonlinear, then X is not a matrix, so this expression wouldn't make sense.

If X is a matrix that maps:

X: point on manifold → vector (direction of flow) on manifold

then this expression makes sense.