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arXiv · 2401.14800

From retraction maps to symplectic-momentum numerical integrators

María Barbero-Liñán·Juan Carlos Marrero·David Martín de Diego
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Abstract

Retraction maps have been generalized to discretization maps in (Barbero Li\~n\'an and and Mart\'{\i}n de Diego, 2022). Discretization maps are used to systematically derive numerical integrators that preserve the symplectic structure, as well as the discrete momemtum map under the assumption of symmetric preservation for the discretization map. The procedure described here gives a geometrical construction that can be easily adapted to discretize dynamics on more general structures and open the door to reduction processes.

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María Barbero-Liñán, Juan Carlos Marrero, David Martín de Diego. 2024-01-26. From retraction maps to symplectic-momentum numerical integrators. https://arxiv.org/abs/2401.14800

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