• Corpus ID: 247218359

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… 
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