Singularities of vector fields

Floris Takens

Displaying similar documents to “Singularities of vector fields”

Smooth linearization of germs of $R^{2}$ -actions and holomorphic vector fields

F. Dumortier, Robert Roussarie (1980)

Annales de l'institut Fourier

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The paper contains a generic condition permitting the linearization in class $𝒞^{k}$ , $0 \leq k \leq \infty$ , of germs of singular infinitesimal $R^{2}$ -actions on $R^{n}$ $(n \geq 2)$ and of singular holomorphic vector fields on $C^{n}$ $(n \geq 1)$ . It generalizes a similar result of S. Sternberg for germs of singular (real) vector fields on $R^{n}$ .

Codimension 4 singularities on reflectionally symmetryc planar vector fields.

Freddy Dumortier, Santiago Ibáñez (1999)

Publicacions Matemàtiques

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The paper deals with the topological classification of singularities of vector fields on the plane which are invariant under reflection with respect to a line. As it has been proved in previous papers, such a classification is necessary to determine the different topological types of singularities of vector fiels on R whose linear part is invariant under rotations. To get the classification we use normal form theory and the the blowing-up method.