Homoclinic orbits on non-compact riemannian manifolds for second order hamiltonian systems
Giannoni, Fabio ; Jeanjean, Louis ; Tanaka, Kazunaga
Rendiconti del Seminario Matematico della Università di Padova, Tome 94 (1995), p. 153-176 / Harvested from Numdam
Publié le : 1995-01-01
@article{RSMUP_1995__93__153_0,
     author = {Giannoni, Fabio and Jeanjean, Louis and Tanaka, Kazunaga},
     title = {Homoclinic orbits on non-compact riemannian manifolds for second order hamiltonian systems},
     journal = {Rendiconti del Seminario Matematico della Universit\`a di Padova},
     volume = {94},
     year = {1995},
     pages = {153-176},
     mrnumber = {1354356},
     zbl = {0845.58031},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RSMUP_1995__93__153_0}
}
Giannoni, Fabio; Jeanjean, Louis; Tanaka, Kazunaga. Homoclinic orbits on non-compact riemannian manifolds for second order hamiltonian systems. Rendiconti del Seminario Matematico della Università di Padova, Tome 94 (1995) pp. 153-176. http://gdmltest.u-ga.fr/item/RSMUP_1995__93__153_0/

[1] A. Ambrosetti - M.L. Bertotti, Homoclinics for second order conservative systems, in Partial Differential Equations and Related Subjects (ed. M. MIRANDA), Pitman Research Note in Math. Ser. (1992). | MR 1190931 | Zbl 0804.34046

[2] A. Ambrosetti - V. Coti Zelati, Multiple homoclinic orbits for a class of conservative systems, Rend. Sem. Mat. Univ. Padova, 89 (1993), pp. 177-194. See also Multiplicité des orbites homoclines pour des Systèmes conservatifs, C. R. Acad. Sci. Paris, 314 (1992), pp. 601-604. | Numdam | MR 1229052 | Zbl 0780.49008

[3] V. Benci - F. GIANNONI, Homoclinic orbits on compact manifolds, J. Math. Anal. Appl., 157 (1991), pp. 568-576. | MR 1112335 | Zbl 0737.58052

[4] M.L. Bertotti, Homoclinics for Lagrangian systems on Riemannian manifolds, Dyn. Sys. Appl., 1 (1992), pp. 341-368. | MR 1195916 | Zbl 0769.58020

[5] P. Caldiroli, Existence and multiplicity of homoclinic orbits for singular potentials on unbounded domains, Proc. Roy. Soc. Edinburgh (to appear). | Zbl 0807.34058

[6] V. Coti Zelati - I. Ekeland - E. Séré, A variational approach to homoclinic orbits in Hamiltonian systems, Math. Ann., 288 (1990), pp. 133-160. | MR 1070929 | Zbl 0731.34050

[7] V. Coti Zelati - P.H. Rabinoeitz, Homoclinic orbits for second order Hamiltonian systems possessing superquadratic potentials, J. Amer. Math. Soc., 4 (1991), pp. 693-727. | MR 1119200 | Zbl 0744.34045

[8] F. Giannoni, On the existence of homoclinic orbits on Riemannian manifolds, Ergodic Theo. Dyn. Sys., 14 (1994), pp. 103-127. | MR 1268711 | Zbl 0796.58026

[9] F. Giannoni - P.H. Rabinowitz, On the multiplicity of homoclinic orbits on Riemannian manifolds for a class of second order Hamiltonian system, Nonlinear Diff. Eq. Appl., 1 (1994), pp. 1-46. | MR 1273342 | Zbl 0823.34050

[10] H. Hofer - K. WYSOCKI, First order elliptic systems and the existence of homoclinic orbits in Hamiltonian system, Math. Ann., 288 (1990), pp. 483-503. | MR 1079873 | Zbl 0702.34039

[11] L. Jeanjean, Existence of connecting orbits in a potential well, Dyn. Sys. Appl. (to appear). | MR 1304132 | Zbl 0817.34029

[12] V. Kozlov, Calculus of variations in the large and classical mechanics, Russ. Math. Surv., 40 (1985), pp. 37-71. | MR 786086 | Zbl 0579.70020

[13] J. Nash, The embedding problem for Riemannian manifolds, Ann. Math., 63 (1956), pp. 20-63. | MR 75639 | Zbl 0070.38603

[14] B. O'Neill, Semi-Riemannian Geometry with Applications to Relativity, Academic Press. (1983). | Zbl 0531.53051

[15] R.S. Palais, Morse theory on Hilbert manifolds, Topology, 2 (1963), pp. 299-340. | MR 158410 | Zbl 0122.10702

[16] P.H. Rabinowitz, Periodic and heteroclinic orbits for a periodic Hamiltonian system, Ann. Inst. H. Poincaré: Analyse Non Linéaire, 6 (1989), pp. 331-346. | Numdam | MR 1030854 | Zbl 0701.58023

[17] P.H. Rabinowitz, Homoclinic orbits for a class of Hamiltonian systems, Proc. Roy. Soc. Edinburg, 114 (1990), pp. 33-38. | MR 1051605 | Zbl 0705.34054

[18] P.H. Rabinowitz - K. TANAKA, Some results on connecting orbits for a class of Hamiltonian system, Math. Zeit., 206 (1991), pp. 473-499. | MR 1095767 | Zbl 0707.58022

[19] E. Séré, Existence of infinitely many homoclinic orbits in Hamiltonian systems, Math. Zeit., 209 (1992), pp. 27-42. | MR 1143210 | Zbl 0725.58017

[20] E. Séré, Looking for the Bernoulli shift, Ann. Inst. H. Poincaré: Analyse Non Linéaire (to appear). | Numdam | MR 1249107 | Zbl 0803.58013

[21] E. Séré, Homoclinic orbits in compact hypersurface in R2N of restricted contact type, preprint. | Zbl 0840.34046

[22] K. Tanaka, Homoclinic orbits for a singular second order Hamiltonian system, Ann. Inst. H. Poincaré: Analyse Non Linéaire, 7 (1990), pp. 427-438. | Numdam | MR 1138531 | Zbl 0712.58026

[23] K. Tanaka, Homoclinic orbits in a first order superquadratic Hamiltonian system: Convergence of subharmonic orbits, J. Diff. Eq., 94 (1991), pp. 315-339. | MR 1137618 | Zbl 0787.34041

[24] K. Tanaka, A note on the existence of multiple homoclinic orbits for a perturbed radial potential, Nonlinear Diff. Eq. Appl. (to appear). | MR 1273347 | Zbl 0819.34032