# Retraction maps: a seed of geometric integrators

@inproceedings{Linan2021RetractionMA, title={Retraction maps: a seed of geometric integrators}, author={Ma Lin-an and David Mart{\'i}n de Diego}, year={2021} }

The classical notion of retraction map used to approximate geodesics is extended and rigorously defined to become a powerful tool to construct geometric integrators and it is called discretization map. Using the geometry of the tangent and cotangent bundles, we are able to tangently and cotangent lift such a map so that these lifts inherit the same properties as the original one and they continue to be discretization maps. In particular, the cotangent lift of a discretization map is a natural…

## 2 Citations

Presymplectic integrators for optimal control problems via retraction maps

- MathematicsArXiv
- 2022

Retractions maps are used to define a discretization of the tangent bundle of the configuration manifold as two copies of the configuration manifold where the dynamics take place. Such discretization…

Geometric Methods for Adjoint Systems

- Mathematics, Computer ScienceArXiv
- 2022

It is shown that the adjoint variational quadratic conservation laws, which are key to adjoint sensitivity analysis, arise from (pre)symplecticity of such adjoint systems, and structure-preserving numerical methods for such systems using Galerkin Hamiltonian variational integrators (Leok and Zhang) are developed.

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