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Une classe d'hamiltoniens polynomiaux isochrones

  Published:2001-09-01
 Printed: Sep 2001
  • Bertrand Schuman
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Abstract

Soit $H_0 = \frac{x^2+y^2}{2}$ un hamiltonien isochrone du plan $\Rset^2$. On met en \'evidence une classe d'hamiltoniens isochrones qui sont des perturbations polynomiales de $H_0$. On obtient alors une condition n\'ecessaire d'isochronisme, et un crit\`ere de choix pour les hamiltoniens isochrones. On voit ce r\'esultat comme \'etant une g\'en\'eralisation du caract\`ere isochrone des perturbations hamiltoniennes homog\`enes consid\'er\'ees dans [L], [P], [S]. Let $H_0 = \frac{x^2+y^2}{2}$ be an isochronous Hamiltonian of the plane $\Rset^2$. We obtain a necessary condition for a system to be isochronous. We can think of this result as a generalization of the isochronous behaviour of the homogeneous polynomial perturbation of the Hamiltonian $H_0$ considered in [L], [P], [S].
Keywords: Hamiltonian system, normal forms, resonance, linearization Hamiltonian system, normal forms, resonance, linearization
MSC Classifications: 34C20, 58F05, 58F22, 58F30 show english descriptions Transformation and reduction of equations and systems, normal forms
unknown classification 58F05
unknown classification 58F22
unknown classification 58F30
34C20 - Transformation and reduction of equations and systems, normal forms
58F05 - unknown classification 58F05
58F22 - unknown classification 58F22
58F30 - unknown classification 58F30
 

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