Computing normal forms and formal invariants of dynamical systems by means of word series Articles uri icon

publication date

  • June 2016

start page

  • 326

end page

  • 345


  • 138

International Standard Serial Number (ISSN)

  • 0362-546X

Electronic International Standard Serial Number (EISSN)

  • 1873-5215


  • We show how to use extended word series in the reduction of continuous and discrete dynamical systems to normal form and in the computation of formal invariants of motion in Hamiltonian systems. The manipulations required involve complex numbers rather than vector fields or diffeomorphisms. More precisely we construct a group (G) over bar and a Lie algebra (g) over bar in such a way that the elements of (G) over bar and (g) over bar are families of complex numbers; the operations to be performed involve the multiplication star in (G) over bar and the bracket of (g) over bar and result in universal coefficients that are then applied to write the normal form or the invariants of motion of the specific problem under consideration. (C) 2015 Elsevier Ltd. All rights reserved.


  • word series; integrable problems; normal forms; trees