Non-integrability of certain Hamiltonian systems. Applications of the Morales-Ramis differential Galois extension of Ziglin theory

• Autorzy: Andrzej J. Maciejewski
• Języki publikacji: EN

Abstrakty

EN

The aim of this paper is to present two examples of non academic Hamiltonian systems for which the Morales-Ramis theory can be applied effectively. First, we investigate the Gross-Neveu system with n degrees of freedom. Till now it has been proved that this system is not integrable for n = 3. We give a simple proof that it is not completely integrable for an arbitrary n ≥ 3. Our second example is a natural generalisation of the Jacobi problem of a material point moving on an ellipsoid. We formulate sufficient conditions for its non-integrability.

Kategorie tematyczne

• 34Mxx: Differential equations in the complex domain
• 70F20: Holonomic systems
• 37J30: Obstructions to integrability (nonintegrability criteria)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2002
• Tom: 58
• Numer: 1
• Strony: 139-150

Daty

wydano

2002

Twórcy

autor

Andrzej J. Maciejewski

• Institute of Astronomy, University of Zielona Góra, Lubuska 2, 65-265 Zielona Góra, Poland

Identyfikatory

DOI

10.4064/bc58-0-10