- #1
geoduck
- 258
- 2
I'm having trouble understanding the exponential map for nonlinear vector fields.
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.
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.