5 citations · 16 across the 7 of their papers we have counts for
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Geometrization of symplecticity conditions for implicit schemes
Hugo Jiménez-Pérez
In this note we give simple symplecticity conditions for implicit schemes in the linear case. We consider implicit maps on generic symplectic manifold and we introduce the concept…
Towards exact symplectic integrators from Liouvillian forms
Hugo Jiménez-Pérez
In this article we introduce a low order implicit symplectic integrator designed to follow the Hamiltonian flow as close as possible. This integrator is obtained by the method of L…
Symplectic maps: from generating functions to Liouvillian forms
Hugo Jiménez-Pérez
In this article we introduce a new method for constructing implicit symplectic maps using special symplectic manifolds and Liouvillian forms. This method extends, in a natural way,…
Symplectic integrators in the realm of Hofer's geometry
Hugo Jiménez-Pérez
Symplectic integrators constructed from Hamiltonian and Lie formalisms are obtained as symplectic maps whose flow follows the exact solution of a "sourrounded" Hamiltonian K = H +…