A Note on the Non-Integrability of Some Hamilitonian Systems with a Homogeneous Potential

• Autores: Juan José Morales Ruiz , Jean Pierre Ramis
• Localización: Methods and applications of analysis, ISSN 1073-2772, Vol. 8, Nº 1, 2001, págs. 113-120
• Idioma: inglés
• DOI: 10.4310/maa.2001.v8.n1.a5
• Texto completo no disponible (Saber más ...)
• Resumen

  • We obtain a non-integrability result on Hamiltonian Systems with a homogeneous potential with an arbitrary number of degrees of freedom which generalizes a Yoshida's Theorem [7]. Except for the cases when the degree of homogeneity of the potential is equal to two or minus two, only a discrete set of families of these type of potentials are compatible with the complete integrability condition. We illustrate this result with two examples: the collinear problem of three bodies and a highly symmetrical family introduced by Umeno ([6]).