2015/10/01 by Ander Murua, Murua, A., J. M. Sanz‐Serna +1
Computer Science · Mathematics · #34C20 #70H05 #Dynamical Systems (math.DS) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Modeling and Simulation Systems #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1510.00250
openalex publication_date 2015/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 and a Lie algebra g in such a way that the elements of G and g are families of complex numbers; the operations to be performed involve the multiplication F in G and the bracket of g 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.