@article{AIHPC_2007__24_3_471_0, author = {Fura, Justyna and Rybicki, S\l awomir}, title = {Periodic solutions of second order hamiltonian systems bifurcating from infinity}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, volume = {24}, year = {2007}, pages = {471-490}, doi = {10.1016/j.anihpc.2006.03.003}, zbl = {1129.37034}, language = {en}, url = {http://dml.mathdoc.fr/item/AIHPC_2007__24_3_471_0} }
Fura, Justyna; Rybicki, Sławomir. Periodic solutions of second order hamiltonian systems bifurcating from infinity. Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) pp. 471-490. doi : 10.1016/j.anihpc.2006.03.003. http://gdmltest.u-ga.fr/item/AIHPC_2007__24_3_471_0/
[1] Lectures on Lie Groups, W.A. Benjamin, New York, 1969. | MR 252560 | Zbl 0206.31604
,[2] Branching points for a class of variational operators, J. Anal. Math. 76 (1998) 321-335. | MR 1676975 | Zbl 0931.47051
,[3] Die Lösung der Versweigungsgleichungen für Nichtlineare Eigenwert-Probleme, Math. Z. 127 (1972) 105-126. | MR 312348
,[4] A Topological Introduction to Nonlinear Analysis, Birkhäuser Boston, Boston, MA, 2004. | MR 2020421 | Zbl 1061.47001
,[5] A new degree for -invariant mappings and applications, Ann. Inst. H. Poincaré Anal. Non Linéaire 2 (5) (1985) 473-486. | Numdam | MR 817033 | Zbl 0579.58022
,[6] Transformation Groups, Walter de Gruyter, Berlin, 1987. | MR 889050 | Zbl 0611.57002
,[7] Existence and continuation of periodic solutions of autonomous Newtonian systems, J. Differential Equations 218 (1) (2005) 216-252. | MR 2174973 | Zbl 1101.34028
, , ,[8] Degree for gradient equivariant maps and equivariant Conley index, in: , (Eds.), Topological Nonlinear Analysis, Degree, Singularity and Variations, Progr. Nonlinear Differential Equations Appl., vol. 27, Birkhäuser, 1997, pp. 247-272. | Zbl 0880.57015
,[9] Hopf bifurcations at infinity, Nonlinear Anal. TMA 13 (12) (1989) 1393-1398. | MR 1028236 | Zbl 0705.34042
,[10] Topological bifurcation, in: , (Eds.), Topological Nonlinear Analysis, Degree, Singularity and Variations, Progr. Nonlinear Differential Equations Appl., vol. 15, Birkhäuser, Basel, 1995, pp. 341-463. | MR 1322327 | Zbl 0899.58010
,[11] Global Bifurcations in Variational Inequalities, Springer-Verlag, New York, 1997. | MR 1438548 | Zbl 0876.49008
, ,[12] Bifurcation from infinity and multiple solutions for periodic boundary value problems, Nonlinear Anal. TMA 42 (1) (2000) 27-39. | MR 1769250 | Zbl 0966.34015
,[13] Periodic trajectories near degenerate equilibria in the Hénon-Heiles and Yang-Mills Hamiltonian systems, J. Dynam. Differential Equations 17 (3) (2005) 475-488. | Zbl 1080.37069
, , ,[14] Periodic solutions of the Liénard equation: bifurcation from infinity and nonuniqueness, Rend. Istit. Mat. Univ. Trieste 19 (1) (1987) 12-31. | MR 941090 | Zbl 0647.34038
,[15] La biforcazione nel caso variazionale, Conf. Sem. Mat. Univ. Bari 132 (1977). | MR 348570 | Zbl 0323.47046
,[16] Symmetries, topological degree and a theorem of Z.Q. Wang, Rocky Mountain J. Math. 24 (3) (1994) 1087-1115. | MR 1307593 | Zbl 0819.47076
,[17] Degenerate branching points of autonomous Hamiltonian systems, Nonlinear Anal. TMA 55 (1-2) (2003) 153-166. | Zbl 1034.37036
,[18] Degenerate bifurcation points of periodic solutions of autonomous Hamiltonian systems, J. Differential Equations 202 (2) (2004) 284-305. | MR 2068442 | Zbl 1076.34042
, ,[19] -degree for orthogonal maps and its applications to bifurcation theory, Nonlinear Anal. TMA 23 (1) (1994) 83-102. | MR 1288500 | Zbl 0815.58027
,[20] Applications of degree for -equivariant gradient maps to variational nonlinear problems with -symmetries, Topol. Methods Nonlinear Anal. 9 (2) (1997) 383-417. | MR 1491852 | Zbl 0891.55003
,[21] Degree for equivariant gradient maps, Milan J. Math. 73 (2005) 103-144. | MR 2175038 | Zbl 1116.58009
,[22] Bifurcations of solutions of -symmetric nonlinear problems with variational structure, in: , , , (Eds.), Handbook of Topological Fixed Point Theory, Springer, Berlin, 2005, pp. 339-372. | MR 2171112 | Zbl 1089.47050
,[23] Hopf bifurcation from infinity, Rend. Sem. Mat. Univ. Padova 78 (1987) 237-253. | Numdam | MR 934515 | Zbl 0644.34037
,[24] Successive bifurcations at infinity for second order O.D.E.'s, Qual. Theory Dynam. Syst. 3 (2) (2002) 1-17. | MR 1960715 | Zbl 1097.34024
,[25] Some remarks on the Böhme-Berger bifurcation theorem, Math. Z. 125 (1972) 359-364. | Zbl 0237.47032
,