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Results tagged with real-analytic-structures
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user 24309
1
vote
Linearization of vector fields
It might be worth mentionning works on linearization/normal-forms of Poisson structures, in particular around a degenerate singular point.
Formes normales de structures de Poisson ayant un 1-jet nul …
- 5,428
2
votes
Accepted
Analyticity of central stable manifolds
Quick answer to the first question: no, there is no reason why it should be analytic. Take e.g. the parametric vector field (written as a Lie derivative)$$X(x,y):=-x^3\partial_x+(y+\alpha x)\partial_y …
- 5,428
3
votes
Polynomial vector field tangent to a given analytic simple closed curve
The answer is "no". In fact, it is still "no" for germs of curves : generically, a germ of an analytic curve $\gamma : (\mathbb R,0)\rightarrow (\mathbb R^2,0)$ is not tangent to any polynomial vector …
- 5,428
5
votes
Are real-analytic functions in $\mathbb{R}^2$ holomorphic after suitable change of coordinates?
To see why the second question cannot have a simple answer, it is sufficient to look at the local context near a fixed-point of a tangent-to-identity mapping, as Alexandre Eremenko suggests. By "a sim …
- 5,428