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Energy Conserving, Liouville, and Symplectic Integrators
Journal of Computational Physics, 1995In the last few years most research in the numerical solution of ordinary differential equations has been addressed to the development of methods adapted to special problems. In particular, a complete theory of symplectic methods for Hamiltonian systems has been constructed [see e.g. \textit{J. M. Sanz-Serna} and \textit{M. P.
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Symplectic Integrators: Rotations and Roundoff Errors
Celestial Mechanics and Dynamical Astronomy, 1998We investigate the numerical implementation of a symplectic integrator combined with a rotation (as in the case of an elongated rotating primary). We show that a straightforward implementation of the rotation as a matrix multiplication destroys the conservative property of the global integrator, due to roundoff errors.
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Integrability of symplectic mappings
2020vıı ABSTRACT INTEGRABILITY OF SYMPLECTIC MAPPINGS This thesis can be divided into two parts: continuous and discrete. In the contin uous part, both finite and infinite dimensional Hamiltonian systems are discussed. In finite dimensional Hamiltonian systems (ODEs) we state the Arnold-Liouvile theorem which gives the conditions of integrability.
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