General information about numerical integration of ordinary differential equations:

[1] Press William H et al., Numerical Recipes 3rd Edition: The Art of Scientific Computing, 3rd ed. (Cambridge University Press, 2007).

[2] Ernst Hairer, Syvert P. Nørsett, and Gerhard Wanner, Solving Ordinary Differential Equations I: Nonstiff Problems, 2nd ed. (Springer, Berlin, 2009).

[3] Ernst Hairer and Gerhard Wanner, Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems, 2nd ed. (Springer, Berlin, 2010).

Symplectic integration of numerical integration:

[4] Ernst Hairer, Gerhard Wanner, and Christian Lubich, Geometric Numerical Integration: Structure-Preserving Algorithms for Ordinary Differential Equations, 2nd ed. (Springer-Verlag Gmbh, 2006).

[5] Leimkuhler Benedict and Reich Sebastian, Simulating Hamiltonian Dynamics (Cambridge University Press, 2005).

Special symplectic methods:

[6] Haruo Yoshida, “Construction of higher order symplectic integrators,” Physics Letters A 150, no. 5 (November 12, 1990): 262-268.

[7] Robert I. McLachlan, “On the numerical integration of ordinary differential equations by symmetric composition methods,” SIAM J. Sci. Comput. 16, no. 1 (1995): 151-168.

Special systems:

[8] Fermi-Pasta-Ulam nonlinear lattice oscillations

[9] Arkady Pikovsky, Michael Rosemblum, and Jürgen Kurths, Synchronization: A Universal Concept in Nonlinear Sciences. (Cambridge University Press, 2001).