Vecteurs propres de matrices de Jacobi
Annales de l'Institut Fourier, Volume 44 (1994) no. 5, p. 1505-1517

It is shown that the set of symmetric tridiagonal periodic Jacobi matrices of given spectrum has a preferred tangent vector field, constructed using the eigenvectors of the matrices and the Jacobian of a hyperelliptic curve. It turns out that this preferred vector field is the infinitesimal operator of the celebrated periodic Toda flow.

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.

@article{AIF_1994__44_5_1505_0,
     author = {Audin, Mich\`ele},
     title = {Vecteurs propres de matrices de Jacobi},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {44},
     number = {5},
     year = {1994},
     pages = {1505-1517},
     doi = {10.5802/aif.1443},
     zbl = {0816.58020},
     mrnumber = {96e:58068},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1994__44_5_1505_0}
}
Audin, Michèle. Vecteurs propres de matrices de Jacobi. Annales de l'Institut Fourier, Volume 44 (1994) no. 5, pp. 1505-1517. doi : 10.5802/aif.1443. http://www.numdam.org/item/AIF_1994__44_5_1505_0/

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