I'm having trouble understanding the exponential map for nonlinear vector fields.(adsbygoogle = window.adsbygoogle || []).push({});

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.

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# Exponential map

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