Morse Theory
Critical points · Gradient flow · Topological invariants of smooth functions
Surface
Torus height
Double saddle
Gaussian bumps
Mexican hat
Flow Steps
80
Contour Lines
15
Show Flow
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Gradient flow:
ẋ = −∇f(x)
Morse inequality:
#minima − #saddles + #maxima = χ
Index:
k = # negative eigenvalues of Hessian
Maximum
Saddle
Minimum
Gradient flow