TY - JOUR
T1 - Linearised higher variational equations
AU - Simon, Sergi
N1 - This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Discrete and Continuous Dynamical Systems following peer review. The definitive publisher-authenticated version Linearised higher variational equations. Simon, S. Nov 2014 In : Discrete and Continuous Dynamical Systems. 34, 11, p. 4827-4854 is available online at: http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=9945
PY - 2014/11/1
Y1 - 2014/11/1
N2 - This work explores the tensor and combinatorial constructs underlying
the linearised higher-order variational equations LVEkψ of a generic autonomous system along a particular solution ψ . The main result of this paper is a compact yet explicit and computationally amenable form for said variational systems and their monodromy matrices. Alternatively, the same methods are useful to retrieve, and sometimes simplify, systems satisfied by the coefficients of the Taylor expansion of a formal first integral for a given dynamical system. This is done in preparation for further results within Ziglin-Morales-Ramis theory, specifically those of a constructive nature.
AB - This work explores the tensor and combinatorial constructs underlying
the linearised higher-order variational equations LVEkψ of a generic autonomous system along a particular solution ψ . The main result of this paper is a compact yet explicit and computationally amenable form for said variational systems and their monodromy matrices. Alternatively, the same methods are useful to retrieve, and sometimes simplify, systems satisfied by the coefficients of the Taylor expansion of a formal first integral for a given dynamical system. This is done in preparation for further results within Ziglin-Morales-Ramis theory, specifically those of a constructive nature.
UR - http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=9945
U2 - 10.3934/dcds.2014.34.4827
DO - 10.3934/dcds.2014.34.4827
M3 - Article
SN - 1078-0947
VL - 34
SP - 4827
EP - 4854
JO - Discrete and Continuous Dynamical Systems
JF - Discrete and Continuous Dynamical Systems
IS - 11
ER -