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On montre que l’ensemble des matrices tridiagonales périodiques symétriques de spectre fixé possède une direction tangente privilégiée, construite à l’aide des vecteurs propres des matrices et de la jacobienne d’une courbe hyperelliptique. Il se trouve que cette direction est celle du célèbre flot de Toda périodique.
The paper deals with 2-parameter families of planar vector fields which are invariant under the group for q ≥ 3. The germs at z = 0 of such families are studied and versal families are found. We also give the phase portraits of the versal families.
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