Nayfeh, A. H., and Mook, D. T., 1979, "*Nonlinear Oscillations*", Wiley Interscience, New York.

Holmes, P., 1986, “Chaotic Motions in a Weakly Nonlinear Model for Surface Waves,” J. Fluid Mech., 162 , pp. 365–388.

McRobie, F. A., Popov, A. A., and Thompson, J. M., 1999, “Auto-parametric Resonance in Cylindrical Shells Using Geometric Averaging,” J. Sound Vib.

[CrossRef], 227 (1), pp. 65–84.

Popov, A. A., Thompson, J. M., and McRobie, F. A., 2001, “Chaotic Energy Exchange Through Auto-Parametric Resonance in Cylindrical Shells,” J. Sound Vib.

[CrossRef], 248 (3), pp. 395–411.

Popov, A. A., 2004, “Autoparametric Resonance in Thin Cylinderical Shells Using the Slow Fluctuation Method,” Thin-Walled Struct., 42 (3), pp. 475–495.

Haxton, R. S., and Barr, A. D., 1972, “The Autoparametric Vibration Absorber,” ASME J. Eng. Ind., 94 , pp. 119–225.

Ikeda, T., 2003, “Nonlinear Parametric Vibrations of an Elastic Structure With a Rectangular Liquid Tank,” Nonlinear Dyn., 33 , pp. 43–70.

Tondl, A., Ruijgrok, T., Verhulst, F., and Nabergoj, R., 2000, "*Autoparametric Resonance in Mechanical Systems*", Cambridge University Press, New York.

Wang, F., Bajaj, A. K., and Kamiya, K., 2005, “Nonlinear Normal Modes and Their Bifurcations for an Inertially Coupled Nonlinear Conservative System,” Nonlinear Dyn. (to appear).

Bajaj, A. K., Chang, S. I., and Johnson, J. M., 1994, “Amplitude Modulated Dynamics of a Resonantly Excited Autoparametric Two Degree-of-Freedom System,” Nonlinear Dyn., 5 , pp. 433–457.

Vyas, A., and Bajaj, A. K., 2001, “Dynamics of Autoparametric Vibration Absorbers Using Multiple Pendulums,” J. Sound Vib., 246 , pp. 115–135.

Vyas, A., Bajaj, A. K., and Raman, A., 2004, “Dynamics of Flexible Structures With Wideband Autoparametric Vibration Absorbers: Theory,” Proc. R. Soc. London, Ser. A, 460 , pp. 1547–1581.

Vyas, A., Bajaj, A. K., and Raman, A., 2004, “Dynamics of Flexible Structures With Wideband Autoparametric Vibration Absorbers: Experiment,” Proc. R. Soc. London, Ser. A, 460 , pp. 1857–1880.

Wiggins, S., 1990, "*Introduction to Applied Nonlinear Dynamical Systems and Chaos*", Springer Verlag, New York.

Banerjee, B., and Bajaj, A. K., 1997, “Amplitude Modulated Chaos in Two Degree-of-Freedom Systems With Quadratic Nonlinearities,” Acta Mech.

[CrossRef], 124 , pp. 131–154.

Tien, W., Namachchivaya, N. S., and Bajaj, A. K., 1994, “Nonlinear Dynamics of a Shallow Arch Under Periodic Excitation. Part I: 1:2 Internal Resonance,” Int. J. Non-Linear Mech., 29 , pp. 349–366.

Wiggins, S., 1988, "*Global Bifurcations and Chaos*", Springer Verlag, New York.

Goldstein, H., 1980, "*Classical Mechanics*", Addison-Wesley, Reading, Ma.

Tabor, M., 1990, "*Chaos and Integrability in Nonlinear Dynamics*", Wiley, New York.

Verhulst, F., 1983, “Asymptotic Analysis of Hamiltonian Systems,” "*Asymptotic Analysis II: Surveys and New Trends*", F.Verhulst, ed., Springer-Verlag, New York, Lecture Notes in Mathematics , Vol. 985 , pp. 137–186.

Van der Aa, E., and Sanders, J. A., 1979. “The 1:2:1-Resonance, Its Periodic Orbits and Integrals”. In "*Asymptotic Analysis from Theory to Applications*", F.Verhulst, ed., Springer-Verlag, Lecture Notes in Mathematics , Vol. 711 , pp. 187–208.

Van der Aa, E., 1983, “First Order Resonances in Three-Degrees-of-Freedom systems,” Celest. Mech., 31 , pp. 163–191.

Wang, L., Bosley, D. L., and Kevorkian, J., 1995, “Asymptotic Analysis of a Class of Three-Degree-of-Freedom Hamiltonian Systems Near Stable equilibria,” Physica D

[CrossRef], 88 , pp. 87–115.

Haller, G., and Wiggins, S., 1996, “Geometry and Chaos Near Resonant Equilibria of 3-DOF Hamiltonian Systems,” Physica D, 90 , pp. 319–365.

Litvak-Hinenzon, A., and Rom-Kedar, V., 2002, “Resonant Tori and Instabilities in Hamiltonian Systems,” Nonlinearity

[CrossRef], 15 , pp. 1149–1177.

Duistermaat, J. J., 1984, “Non-Integrability of the 1:1:2 Resonance,” Ergod. Theory Dyn. Syst.

[CrossRef], 4 , pp. 553–568.

Wiesenfeld, L., 2004, “Local Separatrices for Hamiltonians With Symmetries,” J. Phys. A

[CrossRef], 37 , pp. L143–L149.

Popov, A. A., 2004, “The Application of Hamiltonian Dynamics and Averaging to Nonlinear Shell Vibration,” Comput. Struct., 82 , pp. 2659–2670.

Lynch, P., and Houghton, C., 2004, “Pulsation and Precession of the Resonant Swinging Spring,” Physica D

[CrossRef], 190 , pp. 38–62.