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Hopf Algebra Techniques to Handle Dynamical Systems and Numerical Integrators

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

Abstract

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.

Notes

Acknowledgements

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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Copyright information

© Springer Nature Switzerland AG 2018

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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