Periodic solutions of second order hamiltonian systems bifurcating from infinity

Fura, Justyna; Rybicki, Sławomir

doi:10.1016/j.anihpc.2006.03.003

Fura, Justyna ; Rybicki, Sławomir

Annales de l'I.H.P. Analyse non linéaire, Tome 24 (2007) no. 3, pp. 471-490

Zbl | 1 citation dans Numdam

DOI : 10.1016/j.anihpc.2006.03.003

@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},
     pages = {471--490},
     year = {2007},
     publisher = {Elsevier},
     volume = {24},
     number = {3},
     doi = {10.1016/j.anihpc.2006.03.003},
     zbl = {1129.37034},
     language = {en},
     url = {https://www.numdam.org/articles/10.1016/j.anihpc.2006.03.003/}
}

TY  - JOUR
AU  - Fura, Justyna
AU  - Rybicki, Sławomir
TI  - Periodic solutions of second order hamiltonian systems bifurcating from infinity
JO  - Annales de l'I.H.P. Analyse non linéaire
PY  - 2007
SP  - 471
EP  - 490
VL  - 24
IS  - 3
PB  - Elsevier
UR  - https://www.numdam.org/articles/10.1016/j.anihpc.2006.03.003/
DO  - 10.1016/j.anihpc.2006.03.003
LA  - en
ID  - AIHPC_2007__24_3_471_0
ER  -

%0 Journal Article
%A Fura, Justyna
%A Rybicki, Sławomir
%T Periodic solutions of second order hamiltonian systems bifurcating from infinity
%J Annales de l'I.H.P. Analyse non linéaire
%D 2007
%P 471-490
%V 24
%N 3
%I Elsevier
%U https://www.numdam.org/articles/10.1016/j.anihpc.2006.03.003/
%R 10.1016/j.anihpc.2006.03.003
%G en
%F 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) no. 3, pp. 471-490. doi: 10.1016/j.anihpc.2006.03.003

Bibliographie
Cité par

[1] Adams J.F., Lectures on Lie Groups, W.A. Benjamin, New York, 1969. | Zbl | MR

[2] Ambrosetti A., Branching points for a class of variational operators, J. Anal. Math. 76 (1998) 321-335. | Zbl | MR

[3] Böhme R., Die Lösung der Versweigungsgleichungen für Nichtlineare Eigenwert-Probleme, Math. Z. 127 (1972) 105-126. | MR

[4] Brown R.F., A Topological Introduction to Nonlinear Analysis, Birkhäuser Boston, Boston, MA, 2004. | Zbl | MR

[5] Dancer E.N., A new degree for $SO (2)$ -invariant mappings and applications, Ann. Inst. H. Poincaré Anal. Non Linéaire 2 (5) (1985) 473-486. | Zbl | MR | Numdam

[6] Tom Dieck T., Transformation Groups, Walter de Gruyter, Berlin, 1987. | Zbl | MR

[7] Fura J., Ratajczak A., Rybicki S., Existence and continuation of periodic solutions of autonomous Newtonian systems, J. Differential Equations 218 (1) (2005) 216-252. | Zbl | MR

[8] GȩBa K., Degree for gradient equivariant maps and equivariant Conley index, in: Matzeu M., Vignoli A. (Eds.), Topological Nonlinear Analysis, Degree, Singularity and Variations, Progr. Nonlinear Differential Equations Appl., vol. 27, Birkhäuser, 1997, pp. 247-272. | Zbl

[9] Glover J.N., Hopf bifurcations at infinity, Nonlinear Anal. TMA 13 (12) (1989) 1393-1398. | Zbl | MR

[10] Ize J., Topological bifurcation, in: Matzeu M., Vignoli A. (Eds.), Topological Nonlinear Analysis, Degree, Singularity and Variations, Progr. Nonlinear Differential Equations Appl., vol. 15, Birkhäuser, Basel, 1995, pp. 341-463. | Zbl | MR

[11] Le V.K., Schmitt K., Global Bifurcations in Variational Inequalities, Springer-Verlag, New York, 1997. | Zbl | MR

[12] Ma R., Bifurcation from infinity and multiple solutions for periodic boundary value problems, Nonlinear Anal. TMA 42 (1) (2000) 27-39. | Zbl | MR

[13] Maciejewski A., Radzki W., Rybicki S., Periodic trajectories near degenerate equilibria in the Hénon-Heiles and Yang-Mills Hamiltonian systems, J. Dynam. Differential Equations 17 (3) (2005) 475-488. | Zbl

[14] Malaguti L., Periodic solutions of the Liénard equation: bifurcation from infinity and nonuniqueness, Rend. Istit. Mat. Univ. Trieste 19 (1) (1987) 12-31. | Zbl | MR

[15] Marino A., La biforcazione nel caso variazionale, Conf. Sem. Mat. Univ. Bari 132 (1977). | Zbl | MR

[16] Rabier P., Symmetries, topological degree and a theorem of Z.Q. Wang, Rocky Mountain J. Math. 24 (3) (1994) 1087-1115. | Zbl | MR

[17] Radzki W., Degenerate branching points of autonomous Hamiltonian systems, Nonlinear Anal. TMA 55 (1-2) (2003) 153-166. | Zbl

[18] Radzki W., Rybicki S., Degenerate bifurcation points of periodic solutions of autonomous Hamiltonian systems, J. Differential Equations 202 (2) (2004) 284-305. | Zbl | MR

[19] Rybicki S., $SO (2)$ -degree for orthogonal maps and its applications to bifurcation theory, Nonlinear Anal. TMA 23 (1) (1994) 83-102. | Zbl | MR

[20] Rybicki S., Applications of degree for $SO (2)$ -equivariant gradient maps to variational nonlinear problems with $SO (2)$ -symmetries, Topol. Methods Nonlinear Anal. 9 (2) (1997) 383-417. | Zbl | MR

[21] Rybicki S., Degree for equivariant gradient maps, Milan J. Math. 73 (2005) 103-144. | Zbl | MR

[22] Rybicki S., Bifurcations of solutions of $SO (2)$ -symmetric nonlinear problems with variational structure, in: Brown R., Furi M., Górniewicz L., Jiang B. (Eds.), Handbook of Topological Fixed Point Theory, Springer, Berlin, 2005, pp. 339-372. | Zbl | MR

[23] Sabatini M., Hopf bifurcation from infinity, Rend. Sem. Mat. Univ. Padova 78 (1987) 237-253. | Zbl | MR | Numdam

[24] Sabatini M., Successive bifurcations at infinity for second order O.D.E.'s, Qual. Theory Dynam. Syst. 3 (2) (2002) 1-17. | Zbl | MR

[25] Takens F., Some remarks on the Böhme-Berger bifurcation theorem, Math. Z. 125 (1972) 359-364. | Zbl

Cité par Sources :