TY - JOUR
T1 - The Michelson system is neither global analytic, nor Darboux integrable
AU - Llibre, Jaume
AU - Valls, Clàudia
PY - 2010/4/15
Y1 - 2010/4/15
N2 - We consider the differential system over(x, ̇) = y, over(y, ̇) = z, over(z, ̇) = c2 - y - x2 / 2 in R3, where c is a real parameter. This differential system is known as the Michelson system and its dynamics has been studied during these last twenty five years but nothing was known up to now on its integrability. We show that for any value of c the Michelson system is neither global analytic, nor Darboux integrable. © 2010 Elsevier B.V. All rights reserved.
AB - We consider the differential system over(x, ̇) = y, over(y, ̇) = z, over(z, ̇) = c2 - y - x2 / 2 in R3, where c is a real parameter. This differential system is known as the Michelson system and its dynamics has been studied during these last twenty five years but nothing was known up to now on its integrability. We show that for any value of c the Michelson system is neither global analytic, nor Darboux integrable. © 2010 Elsevier B.V. All rights reserved.
KW - Analytic integrability
KW - Darboux integrability
KW - Darboux polynomials
KW - Exponential factors
KW - Michelson system
KW - Polynomial integrability
KW - Rational integrability
U2 - 10.1016/j.physd.2010.01.007
DO - 10.1016/j.physd.2010.01.007
M3 - Article
SN - 0167-2789
VL - 239
SP - 414
EP - 419
JO - Physica D: Nonlinear Phenomena
JF - Physica D: Nonlinear Phenomena
ER -