## Continuous versus discrete structures II -- Discrete Hamiltonian systems and Helmholtz conditions

*Cresson, Jacky*;

*Pierret, Frédéric*;

- Subject: Mathematics - Dynamical Systems | Mathematics - Numerical Analysisacm: ComputingMethodologies_SIMULATIONANDMODELING

- References (15) 15 references, page 1 of 2
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- 2

[1] I.D. Albu and D. Opri¸s. Helmholtz type condition for mechanical integrators. Novi Sad J. Math., 29(3):11-21, 1999. XII Yugoslav Geometric Seminar (Novi Sad, 1998).

[2] V. I. Arnold. Mathematical methods of classical mechanics, volume 60 of Graduate Texts in Mathematics. Springer-Verlag, New York, 1979.

[3] Z. Bartosiewicz, U. Kotta, E. Pawluszewicz, M. Wyrwas, Algebraic formalism of differntial oneforms for nonlinear control systems on time scales, Proc. Estonian Acad. Sci. Phys. Math., 2007, 56, 3, 264-282.

[4] Bismut, J-M. 1981, M´ecanique al´eatoire, Lecture notes in mathematics (Springer-Verlag).

[5] L. Bourdin, J. Cresson. Helmholtz's inverse problem of the discrete calculus of variations. Journal of Difference Equations and Applications, 19(9):1417-1436, 2013.

[6] J. Cresson, F. Pierret, Discrete versus continuous structures I - Discrete embedding and differential equations, arXiv:1411.7117, 2014.

[7] D. Cr˘aciun and D. Opri¸s. The Helmholtz conditions for the difference equations systems. Balkan J. Geom. Appl., 1(2):21-30, 1996.

[8] S. Lall, M. West, Discrete variational Hamiltonian mechanics, J. Phys. A : Math. Gen. 39 (2006), 5509-5519.

[9] E. Hairer, C. Lubich, and G. Wanner. Geometric numerical integration, volume 31 of Springer Series in Computational Mathematics. Springer-Verlag, Berlin, second edition, 2006. Structurepreserving algorithms for ordinary differential equations.

[10] P.E. Hydon, E.L. Mansfeld, A variational complex for difference equations, 44.p.

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