Poincaré, H., 1892, "*Les Methods Nouvelles de la Mechanique Celeste*", Gauthier-Villars, Paris.

Birkhoff, G. D., 1927, "*Dynamical Systems*", American Mathematical Society, New York.

Arnold, V. I., 1989, "*Mathematical Methods of Classic Mechanics*". Springer-Verlag, Berlin.

Arnold, V. I., 1964, “Instability of Dynamical Systems With Several Degrees of Freedom,” Sov. Math. Dokl., 5 , pp. 581–585.

Henon, M., and Heiles, C., 1964, “The Applicability of the Third Integral Motion: Some Numerical Experiments,” Astron. J.

[CrossRef], 69 , pp. 73–79.

Walker, G. H., and Ford, J., 1969, “Amplitude Instability and Ergodic Behavior for Conservative Nonlinear Oscillator Systems,” Phys. Rev.

[CrossRef], 188 , pp. 416–432.

Melnikov, V. K., 1962, “On the Behavior of Trajectories of System Near to Autonomous Hamiltonian Systems,” Sov. Math. Dokl., 3 , pp. 109–112.

Melnikov, V. K., 1963, “On the Stability of the Center for Time Periodic Perturbations,” Trans. Mosc. Math. Soc., 12 , pp. 1–57.

Filonenko, N. N., Sagdeev, R. Z., and Zaslavsky, G. M., 1967, “Destruction of Magnetic Surfaces by Magnetic Field Irregularities: Part II,” Nucl. Fusion, 7 , pp. 253–266.

Zaslavsky, G. M., and Filonenko, N. N., 1968, “Stochastic Instability of Trapped Particles and Conditions of Application of the Quasi-Linear Approximation,” Sov. Phys. JETP, 27 , pp. 851–857.

Zaslavsky, G. M., 1967, “Stochastic Instability of Nonlinear Oscillations,” J. Appl. Mech. Tech. Phys., 2 , pp. 16–22.

Zaslavsky, G. M., and Chirikov, B. V., 1972, “Stochastic Instability of Nonlinear Oscillations,” Sov. Phys. Usp., 52 , pp. 263–272.

Chirikov, B. V., 1979, “A Universal Instability of Many-Dimensional Oscillator Systems,” Phys. Rep.

[CrossRef], 52 , pp. 263–379.

Escande, D. F., and Doveil, F., 1981, “Renormalization Method for the Onset of Stochasticity in a Hamiltonian System,” Phys. Lett.

[CrossRef], 83A , pp. 307–310.

Escande, D. F., 1985, “Stochasticity in Classic Hamiltonian Systems: Universal Aspects,” Phys. Rep.

[CrossRef], 121 , pp. 165–261.

Luo, A. C. J., 1995, “Analytical Modeling of Bifurcations, Chaos, and Multifractals in Nonlinear Dynamics,” Ph.D. dissertation, University of Manitoba, Winnipeg.

Luo, A. C. J., and Han, R. P. S., 2001, “The Resonance Theory for Stochastic Layers in Nonlinear Dynamical Systems,” Chaos, Solitons Fractals

[CrossRef], 12 , pp. 2493–2508.

Luo, A. C. J., Gu, K., and Han, R. P. S., 1999, “Resonant-Separatrix Webs in Stochastic Layers of the Twin-Well Duffing Oscillator.” Nonlinear Dyn.

[CrossRef], 19 , pp. 37–48.

Han, R. P. S., and Luo, A. C. J., 1998, “Resonant Layers in Nonlinear Dynamics,” ASME J. Appl. Mech., 65 , pp. 727–736.

Luo, A. C. J., 2002, “Resonant Layers in a Parametrically Excited Pendulum.” Int. J. Bifurcation Chaos Appl. Sci. Eng.

[CrossRef], 12 (2), pp. 409–419.

Luo, A. C. J., 2004, “Nonlinear Dynamics Theory of Stochastic Layers in Nonlinear Hamiltonian,” Appl. Mech. Rev.

[CrossRef], 57 , pp. 161–172.

Gidea, M., and Deppe, F., 2006, “Chaotic Orbits in a Restricted Three-Body Problem: Numerical Experiments and Heuristics,” Commun. Nonlinear Sci. Numer. Simul., 11 , pp. 161–171.