[1] Andrés R., Periodic solutions in the generalized Sitnikov (N +1)-body problem, SIAM Journal on Applied Dynamical Systems, 2013, 12(3):1515-1540.
[2] Belbruno E., Llibre J., Mercé O., On the families of periodic orbits which bifurcate from the circular Sitnikov motions, Celestial Mechanics and Dynamical Astronomy, 1994, 60(1):99-129.
[3] Bountis T., Papadakis K., The stability of vertical motion in the N-body circular Sitnikov problem, Celestial Mechanics and Dynamical Astronomy, 2009, 104(1):205-225.
[4] Cen X. L., Cheng X. H., Huang Z. T., et al., On the stability of symmetric periodic orbits of the elliptic Sitnikov problem, SIAM J. Applied Dynamical Systems, 2020, 19:1271-1290.
[5] Cheng X. H., She Z. K., Study on chaotic behavior of the restricted four-Body problem with an equilateral triangle configuration, International Journal of Bifurcation and Chaos, 2017, 27(2):1750026, 12 pp.
[6] Corbera M., Llibre J., Periodic orbits of the Sitnikov problem via a Poincaré map, Celestial Mechanics and Dynamical Astronomy, 2000, 77:273-303.
[7] Corbera M., Llibre J., On symmetric periodic orbits of the elliptic Sitnikov problem via the analytic continuation method, MR1884894, Contemporary Mathematics, 2002, 292:91-127.
[8] Dankowicz H., Holmes P., The existence of transverse homoclinic points in the Sitnikov problem, Journal of Differential Equations, 1995, 116:468-483.
[9] Galán J., Núñez D., Rivera A., Quantitative stability of certain families of periodic solutions in the Sitnikov problem, SIAM Journal on Applied Dynamical Systems, 2018, 17:52-77.
[10] Galán J., Núñez D., Rivera A., et al., Stability and bifurcations of even periodic orbits in the Sitnikov problem, Celestial Mechanics and Dynamical Astronomy, 2018, 130:82, 20 pp.
[11] Guckenhermer J., Holmes P., Nonlinear Osicillations, Dynamical Systems, and Bifurcations of Vector Fields, Springer-Verlag, New York, 1983.
[12] Jiménez-Lara L., Escalona-BuendÍa A., Symmetries and bifurcations in the Sitnikov problem, Celestial Mechanics and Dynamical Astronomy, 2001, 79:97-117.
[13] Llibre J., Perez-Chavela E., Transversal homoclinic orbits in the collinear restricted three-body problem, Journal of Nonlinear Science, 2005, 15(1):1-10.
[14] Llibre J., Ortega R., On the families of periodic orbits of the Sitnikov problem, SIAM Journal on Applied Dynamical Systems, 2008, 7(2):561-576.
[15] Macmillan W., An integrable case in the restricted problem of three bodies, Astronomical Journal, 1911, 27(625):11-13.
[16] Markellos V., Bifurcations of straight line oscillations, Astronomy and Astrophysics, 1978, 67:229-240.
[17] McGehee R., A stable manifoid theorem for degenerate fixed points with Applications to Celestial Mechanics, Differential Equations, 1973, 14:70-88.
[18] Misquero M., Resonance tongues in the linear Sitnikov equation, Celestial Mechanics and Dynamical Astronomy, 2018, 130(4):25 pp.
[19] Moser J., Stable and Random Motion in Dynamical Systems, Princeton University Press, Princeton, 1973.
[20] Ortega R., Symmetric periodic solutions in the Sitnikov problem, Archiv der Mathematik, Basel, 2016, 107:405-412.
[21] Prudnikov A., Brychkov Y., Marichev O., Integrals and Series I, Gordon and Breach Science Publishers, New York, 1986.
[22] Shang D. S., Zhang Y. M., Bifurcation in a cubic system with a degenerate saddle point, International Journal of Bifurcation and Chaos, 2014, 24(11):1450144, 13 pp.
[23] She Z. K., Cheng X. H., Li C. P., The existence of transversal homoclinic orbits in a planar circular restricted four-body problem, Celestial Mechanics and Dynamical Astronomy, 2013, 115(3):299-309.
[24] She Z. K., Cheng X. H., The existence of the Smale horseshoe in a planar circular restricted four-body problem, Celestial Mechanics and Dynamical Astronomy, 2014, 118(2):115-127.
[25] Sitnikov K., The existence of oscillatory motions in the three-body problems, Doklady Akad. Nauk SSSR, 1960, 133:303-306.
[26] Szebehely V., Theory of Orbits:The Restricted Problem of Three Bodies, Academic Press, New York, 1967.
[27] Wiggins S., Global Bifurcations and Chaos:Analytical Methods, Springer, New York, 1988.
[28] Wodnar K., Analytical Approximations for Sitnikov's Problem, In:From Newton to Chaos, Springer, New York, 1995, 513-523.
[29] Xia Z. H., Melnikov method and transversal homoclinic points in the restricted three-body problem, Journal of Differential Equations, 1992, 96(1):170-184.
[30] Ilyashenko Y., Li W. G., Nonlocal bifurcations, American Mathematical Society, 1998.
[31] Zhang M., Cen X. H., Cheng X. H., Linearized stability and instability of nonconstant periodic solutions of Lagrangian equations, Mathematical Methods in the Applied Sciences, 2018, 41:4853-4866.
[32] Zhang Z. F., Li C. Z., Zheng Z. M., et al., Bifurcations Theory of the Vector Fields (in Chinese), Higher Education Press, Beijing, 1997.
[33] Zhu R. Z., Xiang C., Studies of Melnikov method and transversal homoclinic orbits in the circular planar restricted three-body problem, Applied Mathematics and Mechanics, 1996, 17:1177-1187.