@article{AIHPC_2007__24_4_589_0, author = {Chen, Chao-Nien and Hu, Xijun}, title = {Maslov index for homoclinic orbits of hamiltonian systems}, journal = {Annales de l'I.H.P. Analyse non lin\'eaire}, pages = {589--603}, publisher = {Elsevier}, volume = {24}, number = {4}, year = {2007}, doi = {10.1016/j.anihpc.2006.06.002}, mrnumber = {2334994}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2006.06.002/} }
TY - JOUR AU - Chen, Chao-Nien AU - Hu, Xijun TI - Maslov index for homoclinic orbits of hamiltonian systems JO - Annales de l'I.H.P. Analyse non linéaire PY - 2007 SP - 589 EP - 603 VL - 24 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2006.06.002/ DO - 10.1016/j.anihpc.2006.06.002 LA - en ID - AIHPC_2007__24_4_589_0 ER -
%0 Journal Article %A Chen, Chao-Nien %A Hu, Xijun %T Maslov index for homoclinic orbits of hamiltonian systems %J Annales de l'I.H.P. Analyse non linéaire %D 2007 %P 589-603 %V 24 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2006.06.002/ %R 10.1016/j.anihpc.2006.06.002 %G en %F AIHPC_2007__24_4_589_0
Chen, Chao-Nien; Hu, Xijun. Maslov index for homoclinic orbits of hamiltonian systems. Annales de l'I.H.P. Analyse non linéaire, Volume 24 (2007) no. 4, pp. 589-603. doi : 10.1016/j.anihpc.2006.06.002. http://www.numdam.org/articles/10.1016/j.anihpc.2006.06.002/
[1] A new cohomology to Morse theory of strongly indefinite functionals on Hilbert spaces, Top. Meth. Nonl. Anal. 9 (1997) 325-382. | MR | Zbl
,[2] Morse Theory for Hamiltonian Systems, Research Notes in Mathematics, vol. 425, Chapman Hall/CRC, 2001. | MR | Zbl
,[3] Index estimates for strongly indefinite functionals, periodic orbits and homoclinic solutions of first order Hamiltonian systems, Calc. Var. 11 (2000) 395-430. | MR | Zbl
, ,[4] A topological invariant arising in the stability analysis of travelling waves, J. Reine Angew. Math. 410 (1990) 167-212. | MR | Zbl
, , ,[5] Homoclinic solutions of Hamiltonian systems with symmetry, J. Differential Equations 158 (1999) 291-313. | MR | Zbl
, ,[6] On a characteristic class entering into the quantization condition, Funkt. Anal. Prilozh. 1 (1967) 1-14, (in Russian). | MR | Zbl
,[7] Spectral asymmetry and Riemannian geometry III, Math. Proc. Cambridge Philos. Soc. 79 (1976) 71-99. | MR | Zbl
, , ,[8] Critical point theorems for indefinite functionals, Invent. Math. 52 (1979) 241-273. | MR | Zbl
, ,[9] On the Maslov index, Comm. Pure Appl. Math. 47 (1994) 121-186. | MR | Zbl
, , ,[10] Infinite Dimensional Morse Theory and Multiple Solution Problems, Birkhäuser, Basel, 1993. | MR | Zbl
,[11] Nontrivial periodic solutions for strong resonance Hamiltonian systems, Ann. Inst. H. Poincaré Anal. Non Linéaire (1997) 103-117. | Numdam | MR | Zbl
, , ,[12] Periodic solutions and their connecting orbits of Hamiltonian systems, J. Differential Equations 177 (2001) 121-145. | MR | Zbl
, ,[13] Homoclinic orbits for a class of infinite-dimensional Hamiltonian systems, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 24 (1997) 367-393. | Numdam | MR | Zbl
, , ,[14] Morse-type index theory for flows and periodic solutions for Hamiltonian equations, Comm. Pure Appl. Math. 37 (1984) 207-253. | MR | Zbl
, ,[15] A variational approach to homoclinic orbits in Hamiltonian systems, Math. Ann. 228 (1990) 133-160. | MR | Zbl
, , ,[16] Homoclinic orbits for first order Hamiltonian systems, J. Math. Anal. Appl. 189 (1995) 585-601. | MR | Zbl
, ,[17] Homoclinic orbits of a Hamiltonian system, Z. Angew. Math. Phys. 50 (1999) 759-778. | MR | Zbl
, ,[18] An index theory for periodic solutions of convex Hamiltonian systems, Proc. Symp. Pure Math. 45 (1986) 395-423. | MR | Zbl
,[19] Convexity Methods in Hamiltonian Mechanics, Springer, Berlin, 1990. | MR | Zbl
,[20] Relative Morse index and its application to Hamiltonian systems in the presence of symmetries, J. Differential Equations 122 (1995) 302-315. | MR | Zbl
,[21] Maslov-type index and periodic solutions of asymptotically linear systems which are resonant at infinity, J. Differential Equations 121 (1995) 121-133. | MR | Zbl
,[22] A relative Morse index for the symplectic action, Comm. Pure Appl. Math. 41 (1988) 393-407. | MR | Zbl
,[23] First order elliptic systems and the existence of homoclinic orbits in Hamiltonian systems, Math. Ann. 228 (1990) 483-503. | MR | Zbl
, ,[24] Symplectic Invariants and Hamiltonian Dynamics, Birkhäuser, The Analysis of Linear Partial Differential Operators, I-IV, Springer, Berlin, 1983. | Zbl
, ,[25] Analysis, GSM, vol. 14, Amer. Math. Soc., 1997. | MR | Zbl
, ,[26] Maslov-type index, degenerate critical points, and asymptotically linear Hamiltonian systems, Sci. China, Ser. A 33 (1990) 1409-1419. | MR | Zbl
,[27] Index Theory for Symplectic Paths with Applications, Birkhäuser, Basel, 2002. | MR | Zbl
,[28] Maslov-type index theory for symplectic paths and spectral flow (II), Chin. Ann. of Math. 21B (1) (2000) 89-108. | MR | Zbl
, ,[29] Closed characteristics on compact convex hypersurfaces in , Ann. of Math. 155 (2002) 317-368. | MR | Zbl
, ,[30] Morse theory for forced oscillations of asymptotically linear Hamiltonian systems, in: Stoc. Proc. Phys. and Geom., World Sci., 1990, pp. 528-563. | MR
, ,[31] Perturbation Theory for Linear Operators, Springer, New York, 1980. | Zbl
,[32] Theory of Perturbations and Asymptotic Methods, MGU, 1965, (in Russian).
,[33] Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math. 31 (1978) 157-184. | MR | Zbl
,[34] Critical point theory and applications to differential equations: A survey, in: Topological Nonlinear Analysis, Progr. Nonlinear Differential Equations Appl., vol. 15, Birkhäuser, Boston, MA, 1995, pp. 464-513. | MR | Zbl
,[35] The Maslov index for paths, Topology 32 (4) (1993) 827-844. | MR | Zbl
, ,[36] The spectral flow and the Maslov index, Bull. London Math. Soc. 27 (1) (1995) 1-33. | MR | Zbl
, ,[37] Morse theory for periodic solutions of Hamiltonian systems and the Maslov index, Comm. Pure Appl. Math. 45 (1992) 1303-1360. | MR | Zbl
, ,[38] Existence of infinitely many homoclinic orbits in Hamiltonian systems, Math. Z. 209 (1992) 27-42. | MR | Zbl
,[39] Looking for the Bernoulli shift, Ann. IHP-Analyse Nonlineaire 10 (1993) 561-590. | Numdam | MR | Zbl
,[40] Homoclinic orbits for asymptotically linear Hamiltonian systems, J. Funct. Anal. 187 (2001) 25-41. | MR | Zbl
, ,[41] Cohomology and Morse theory for strongly indefinite functionals, Math. Z. 209 (1992) 375-418. | MR | Zbl
,[42] Homoclinic orbits in a first order superquadratic Hamiltonian system: Convergence of subharmonic orbits, J. Differential Equations 94 (1991) 315-339. | MR | Zbl
,[43] A new obstruction to embedding Lagrangian tori, Invent. Math. 100 (1990) 301-320. | MR | Zbl
,[44] Maslov-type index theory for symplectic paths and spectral flow (I), Chin. Ann. of Math. 20B (4) (1999) 413-424. | MR | Zbl
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