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Results tagged with singularity-theory
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user 1227
Singularities in algebraic/complex/differential geometry and analysis of ODEs/PDEs. Singular spaces, vector fields, etc.
8
votes
Accepted
What does the Jacobian of a vector field at an equilibrium tell you about local behavior of ...
The Jacobian alone doesn't have the information you need. For example, consider the two vector fields
$$f(x, y) = (-x^2, -y)$$
and
$$g(x, y) = (-x^3, -y)$$.
They have an isolated equilibrium at the or …
- 6,571
7
votes
Accepted
Fibers of generic smooth maps between manifolds of equal dimension
Yes, the claim is true, and here's a reference. For $M$ compact, your condition is satisfied by a "finite mapping." Such finite mappings form a residual set when $\dim M \leq \dim N$. See pp. 167-169 …
- 6,571