Word series for dynamical systems and their numerical integrators Articles uri icon

publication date

  • June 2017

start page

  • 675

end page

  • 712


  • 3


  • 17

International Standard Serial Number (ISSN)

  • 1615-3375

Electronic International Standard Serial Number (EISSN)

  • 1615-3383


  • We study word series and extended word series, classes of formal series for the analysis of some dynamical systems and their discretizations. These series are similar to but more compact than B-series. They may be composed among themselves by means of a simple rule. While word series have appeared before in the literature, extended word series are introduced in this paper. We exemplify the use of extended word series by studying the reduction to normal form and averaging of some perturbed integrable problems. We also provide a detailed analysis of the behavior of splitting numerical methods for those problems.


  • Mathematics


  • word series; hopf algebras; hamiltonian problems; normal forms; averaging; splitting algorithms; oscillatory differential-equations; formal series; b-series; trees