Hopf Algebra Techniques to Handle Dynamical Systems and Numerical Integrators

  • Ander MuruaEmail author
  • Jesús M. Sanz-Serna
Conference paper
Part of the Abel Symposia book series (ABEL, volume 13)


In a series of papers the present authors and their coworkers have developed a family of algebraic techniques to solve a number of problems in the theory of discrete or continuous dynamical systems and to analyze numerical integrators. Given a specific problem, those techniques construct an abstract, universal version of it which is solved algebraically; then, the results are transferred to the original problem with the help of a suitable morphism. In earlier contributions, the abstract problem is formulated either in the dual of the shuffle Hopf algebra or in the dual of the Connes-Kreimer Hopf algebra. In the present contribution we extend these techniques to more general Hopf algebras, which in some cases lead to more efficient computations.



A. Murua and J.M. Sanz-Serna have been supported by projects MTM2013-46553-C3-2-P and MTM2013-46553-C3-1-P from Ministerio de Economía y Comercio, and MTM2016-77660-P(AEI/FEDER, UE) from Ministerio de Economía, Industria y Competitividad, Spain. Additionally A. Murua has been partially supported by the Basque Government (Consolidated Research Group IT649-13).


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Authors and Affiliations

  1. 1.Konputazio Zientziak eta A. A. Saila, Informatika Fakultatea, UPV/EHUDonostia–San SebastiánSpain
  2. 2.Departamento de MatemáticasUniversidad Carlos III de MadridLeganés (Madrid)Spain

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