Critical point
Summary
A critical point of a real function is a point where the derivative is zero or does not exist. All interior local extrema of the function occur at critical points. The node critical point gives the precise definition.
Where this leads
35 pages build on this one.
- Sendov's conjecture
- Stationary phase approximation
- Thom's classification of elementary catastrophes
- Catastrophe theory
- Morse–Bott function
- Milnor fibration theorem
- Isolated hypersurface singularity
- Codimension of a singularity
- Circle map
- Marden's theorem
- Morse index
- Butterfly catastrophe
- Critical point theory
- Fold catastrophe
- Modality of a singularity
- Finite determinacy theorem
- Mountain pass theorem
- Morse lemma
- Nondegenerate critical point
- Lusternik–Schnirelmann theory of critical points
- Cerf theory
- Singularity theory
- Umbilic catastrophes
- Regular value theorem
- Arnold's classification of simple critical points
- Morse function
- Swallowtail catastrophe
- Parametric transversality theorem
- Vanishing cycle
- Bifurcation set
- Cusp catastrophe
- Jakobson's theorem
- Singer's theorem
- Sard–Smale theorem
- Sard's theorem
Further reading
About this page
| Tag | 0YTCMFB4HC |
|---|---|
| URI | m2://0YTCMFB4HC |
| Kind | concept |
| Writing | W1 stated |
| MSC | 26A24 |
| Same as |
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What this page needs for W2
- edge instance_of in: at least two examples (0 of 2)
- edge not_instance_of in: at least one non-example (0 of 1)
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What links here
Definitions
Special cases
Results about this
- Sendov's conjecture
- Milnor fibration theorem
- Marden's theorem
- Mountain pass theorem
- Arnold's classification of simple critical points
- Sard's theorem
Used by
- Sendov's conjecture
- Stationary phase approximation
- Thom's classification of elementary catastrophes
- Catastrophe theory
- Morse–Bott function
- Milnor fibration theorem
- Isolated hypersurface singularity
- Codimension of a singularity
- Circle map
- Marden's theorem
- Morse index
- Butterfly catastrophe
- Critical point theory
- Fold catastrophe
- Modality of a singularity
- Finite determinacy theorem
- Mountain pass theorem
- Morse lemma
- Nondegenerate critical point
- Lusternik–Schnirelmann theory of critical points
- Cerf theory
- Singularity theory
- Umbilic catastrophes
- Arnold's classification of simple critical points
- Morse function
- Swallowtail catastrophe
- Vanishing cycle
- Bifurcation set
- Cusp catastrophe
- Singer's theorem
- Sard's theorem