Geodesic
Une classe d’hamiltoniens polynomiaux isochrones
Canadian mathematical bulletin, Tome 44 (2001) no. 3, pp. 323-334

Voir la notice de l'article provenant de la source Cambridge University Press

Soit ${{H}_{0}}\,=\,\frac{{{x}^{2}}+{{y}^{2}}}{2}$ un hamiltonien isochrone du plan ${{\mathbb{R}}^{2}}$ . On met en évidence une classe d’hamiltoniens isochrones qui sont des perturbations polynomiales de ${{H}_{0}}$ . On obtient alors une condition nécessaire d’isochronisme, et un critère de choix pour les hamiltoniens isochrones. On voit ce résultat comme étant une généralisation du caractère isochrone des perturbations hamiltoniennes homogènes considérées dans $\left[ \text{L} \right],\,\left[ \text{P} \right],\,\left[ \text{S} \right]$ .
DOI : 10.4153/CMB-2001-032-9
Mots-clés : 34C20, 58F05, 58F22, 58F30, Hamiltonian system, normal forms, resonance, linearization 
Schuman, Bertrand. Une classe d’hamiltoniens polynomiaux isochrones. Canadian mathematical bulletin, Tome 44 (2001) no. 3, pp. 323-334. doi: 10.4153/CMB-2001-032-9
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