TY - JOUR AU - Alekseev, V. M. PY - 1968 DA - 1968// TI - Quasirandom dynamical systems. II. One-dimensional nonlinear oscillations in a field with periodic perturbation JO - Math. USSR-Sbornik VL - 6 UR - https://doi.org/10.1070/SM1968v006n04ABEH001074 DO - 10.1070/SM1968v006n04ABEH001074 ID - Alekseev1968 ER - TY - JOUR AU - Alfaro, J. M. AU - Chiralt, C. PY - 1993 DA - 1993// TI - Invariant rotational curves in Sitnikov’s problem JO - Celest. Mech. Dyn. Astron. VL - 55 UR - https://doi.org/10.1007/BF00692994 DO - 10.1007/BF00692994 ID - Alfaro1993 ER - TY - JOUR AU - Belbruno, E. AU - Llibre, J. AU - Ollé, M. PY - 1994 DA - 1994// TI - On the families of periodic orbits which bifurcate from the circular Sitnikov motions JO - Celest. Mech. Dyn. Astron. VL - 60 UR - https://doi.org/10.1007/BF00693095 DO - 10.1007/BF00693095 ID - Belbruno1994 ER - TY - JOUR AU - Beltritti, G. AU - Mazzone, F. AU - Oviedo, M. PY - 2018 DA - 2018// TI - The Sitnikov problem for several primary bodies configurations JO - Celest. Mech. Dyn. Astron. VL - 130 UR - https://doi.org/10.1007/s10569-018-9838-4 DO - 10.1007/s10569-018-9838-4 ID - Beltritti2018 ER - TY - JOUR AU - Bountis, T. AU - Papadakis, K. PY - 2009 DA - 2009// TI - The stability of vertical motion in the n-body circular Sitnikov problem JO - Celest. Mech. Dyn. Astron. VL - 104 UR - https://doi.org/10.1007/s10569-009-9194-5 DO - 10.1007/s10569-009-9194-5 ID - Bountis2009 ER - TY - JOUR AU - Corbera, M. AU - Llibre, J. PY - 2000 DA - 2000// TI - Periodic orbits of the Sitnikov problem via a Poincaré map JO - Celest. Mech. Dyn. Astron. VL - 77 UR - https://doi.org/10.1023/A:1011117003713 DO - 10.1023/A:1011117003713 ID - Corbera2000 ER - TY - JOUR AU - Corbera, M. AU - Llibre, J. PY - 2002 DA - 2002// TI - On symmetric periodic orbits of the elliptic Sitnikov problem via the analytic continuation method JO - Contemp. Math. VL - 292 UR - https://doi.org/10.1090/conm/292/04918 DO - 10.1090/conm/292/04918 ID - Corbera2002 ER - TY - JOUR AU - Dvorak, R. PY - 1993 DA - 1993// TI - Numerical results to the Sitnikov-problem JO - Celest. Mech. Dyn. Astron. VL - 56 UR - https://doi.org/10.1007/BF00699721 DO - 10.1007/BF00699721 ID - Dvorak1993 ER - TY - STD TI - Hartman, P.: Ordinary differential equations, Classics in Applied Mathematics, vol. 38. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA (2002). Corrected reprint of the second (1982) edition ID - ref9 ER - TY - JOUR AU - Jiménez-Lara, L. AU - Escalona-Buendía, A. PY - 2001 DA - 2001// TI - Symmetries and bifurcations in the Sitnikov problem JO - Celest. Mech. Dyn. Astron. VL - 79 UR - https://doi.org/10.1023/A:1011109827402 DO - 10.1023/A:1011109827402 ID - Jiménez-Lara2001 ER - TY - JOUR AU - Llibre, J. AU - Ortega, R. PY - 2008 DA - 2008// TI - On the families of periodic orbits of the Sitnikov problem JO - SIAM J. Appl. Dyn. Syst. VL - 7 UR - https://doi.org/10.1137/070695253 DO - 10.1137/070695253 ID - Llibre2008 ER - TY - STD TI - Llibre, J., Simó, C.: Estudio cualitativo del problema de Sitnikov. Publicacions de la Secció de Matemàtiques, pp. 49–71(1980) ID - ref12 ER - TY - STD TI - Llibre, J., Moeckel, R., Simó, C.: Central configurations, periodic orbits, and Hamiltonian systems. Advanced Courses in Mathematics - CRM Barcelona. Birkhauser (2015) ID - ref13 ER - TY - BOOK AU - Magnus, W. AU - Winkler, S. PY - 2013 DA - 2013// TI - Hill’s Equation PB - Courier Corporation CY - Chelmsford ID - Magnus2013 ER - TY - JOUR AU - Marchesin, M. AU - Vidal, C. PY - 2013 DA - 2013// TI - Spatial restricted rhomboidal five-body problem and horizontal stability of its periodic solutions JO - Celest. Mech. Dyn. Astron. VL - 115 UR - https://doi.org/10.1007/s10569-012-9462-7 DO - 10.1007/s10569-012-9462-7 ID - Marchesin2013 ER - TY - BOOK AU - Moser, J. PY - 1973 DA - 1973// TI - Stable and Random Motions in Dynamical Systems: With Special Emphasis on Celestial Mechanics, Annals Mathematics Studies PB - Princeton University Press CY - Princeton ID - Moser1973 ER - TY - BOOK AU - Murray, C. D. AU - Dermott, S. F. PY - 1999 DA - 1999// TI - Solar System Dynamics PB - Cambridge University Press CY - Cambridge ID - Murray1999 ER - TY - JOUR AU - Ortega, R. PY - 2016 DA - 2016// TI - Symmetric periodic solutions in the Sitnikov problem JO - Archiv der Mathematik VL - 107 UR - https://doi.org/10.1007/s00013-016-0931-1 DO - 10.1007/s00013-016-0931-1 ID - Ortega2016 ER - TY - JOUR AU - Ortega, R. AU - Rivera, A. PY - 2010 DA - 2010// TI - Global bifurcations from the center of mass in the Sitnikov problem JO - Discrete Contin. Dyn. Syst. B VL - 14 UR - https://doi.org/10.3934/dcdsb.2010.14.719 DO - 10.3934/dcdsb.2010.14.719 ID - Ortega2010 ER - TY - JOUR AU - Pandey, L. P. AU - Ahmad, I. PY - 2013 DA - 2013// TI - Periodic orbits and bifurcations in the Sitnikov four-body problem when all primaries are oblate JO - Astrophys. Space Sci. VL - 345 UR - https://doi.org/10.1007/s10509-013-1375-8 DO - 10.1007/s10509-013-1375-8 ID - Pandey2013 ER - TY - JOUR AU - Perdios, E. AU - Markellos, V. V. PY - 1987 DA - 1987// TI - Stability and bifurcations of Sitnikov motions JO - Celest. Mech. Dyn. Astron. VL - 42 UR - https://doi.org/10.1007/BF01232956 DO - 10.1007/BF01232956 ID - Perdios1987 ER - TY - JOUR AU - Rabinowitz, P. H. PY - 1971 DA - 1971// TI - Some global results for nonlinear eigenvalue problems JO - J. Funct. Anal. VL - 7 UR - https://doi.org/10.1016/0022-1236(71)90030-9 DO - 10.1016/0022-1236(71)90030-9 ID - Rabinowitz1971 ER - TY - JOUR AU - Rivera, A. PY - 2013 DA - 2013// TI - Periodic solutions in the generalized Sitnikov $$(n+1)$$(n+1)-body problem JO - SIAM J. Appl. Dyn. Syst. VL - 12 UR - https://doi.org/10.1137/120883876 DO - 10.1137/120883876 ID - Rivera2013 ER - TY - BOOK AU - Rivera, A. AU - Andrés, M. PY - 2012 DA - 2012// TI - Bifurcación de soluciones periódicas en el problema de Sitnikov PB - Universidad de Granada CY - Granada ID - Rivera2012 ER - TY - JOUR AU - Sitnikov, K. PY - 1960 DA - 1960// TI - The existence of oscillatory motions in the three-body problem JO - Dokl. Akad. Nauk SSSR VL - 133 ID - Sitnikov1960 ER - TY - JOUR AU - Soulis, P. S. AU - Papadakis, K. E. AU - Bountis, T. PY - 2008 DA - 2008// TI - Periodic orbits and bifurcations in the Sitnikov four-body problem JO - Celest. Mech. Dyn. Astron. VL - 100 UR - https://doi.org/10.1007/s10569-008-9118-9 DO - 10.1007/s10569-008-9118-9 ID - Soulis2008 ER - TY - JOUR AU - Zanini, C. PY - 2003 DA - 2003// TI - Rotation numbers, eigenvalues, and the Poincaré–Birkhoff theorem JO - J. Math. Anal. Appl. VL - 279 UR - https://doi.org/10.1016/S0022-247X(03)00012-X DO - 10.1016/S0022-247X(03)00012-X ID - Zanini2003 ER -