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

Andrzej J. Maciejewski. "Non-integrability of certain Hamiltonian systems. Applications of the Morales-Ramis differential Galois extension of Ziglin theory." Banach Center Publications 58.1 (2002): 139-150. <http://eudml.org/doc/282361>.

@article{AndrzejJ2002,
abstract = {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.},
author = {Andrzej J. Maciejewski},
journal = {Banach Center Publications},
keywords = {nonintegrability; Morales-Ramis theory; Gross-Neveu system; motion on an ellipsoid},
language = {eng},
number = {1},
pages = {139-150},
title = {Non-integrability of certain Hamiltonian systems. Applications of the Morales-Ramis differential Galois extension of Ziglin theory},
url = {http://eudml.org/doc/282361},
volume = {58},
year = {2002},
}

TY - JOUR
AU - Andrzej J. Maciejewski
TI - Non-integrability of certain Hamiltonian systems. Applications of the Morales-Ramis differential Galois extension of Ziglin theory
JO - Banach Center Publications
PY - 2002
VL - 58
IS - 1
SP - 139
EP - 150
AB - 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.
LA - eng
KW - nonintegrability; Morales-Ramis theory; Gross-Neveu system; motion on an ellipsoid
UR - http://eudml.org/doc/282361
ER -