TY - JOUR
T1 - Non-integrability of Hamiltonian systems through high order variational equations: Summary of results and examples
AU - Martínez, Regina
AU - Simó, Carles
PY - 2009/6/18
Y1 - 2009/6/18
N2 - This paper deals with non-integrability criteria, based on differential Galois theory and requiring the use of higher order variational equations. A general methodology is presented to deal with these problems. We display a family of Hamiltonian systems which require the use of order k variational equations, for arbitrary values of k, to prove non-integrability. Moreover, using third order variational equations we prove the non-integrability of a non-linear spring-pendulum problem for the values of the parameter that can not be decided using first order variational equations. © Pleiades Publishing, Ltd. 2009.
AB - This paper deals with non-integrability criteria, based on differential Galois theory and requiring the use of higher order variational equations. A general methodology is presented to deal with these problems. We display a family of Hamiltonian systems which require the use of order k variational equations, for arbitrary values of k, to prove non-integrability. Moreover, using third order variational equations we prove the non-integrability of a non-linear spring-pendulum problem for the values of the parameter that can not be decided using first order variational equations. © Pleiades Publishing, Ltd. 2009.
U2 - 10.1134/S1560354709030010
DO - 10.1134/S1560354709030010
M3 - Article
VL - 14
SP - 323
EP - 348
JO - Regular and Chaotic Dynamics
JF - Regular and Chaotic Dynamics
SN - 1560-3547
IS - 3
ER -