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Volumn 154, Issue 1, 2000, Pages 76-131

Precise iteration formulae of the Maslov-type index theory and ellipticity of closed characteristics

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EID: 0034259343     PISSN: 00018708     EISSN: None     Source Type: Journal    
DOI: 10.1006/aima.2000.1914     Document Type: Article
Times cited : (110)

References (56)
  • 1
    • 0001283157 scopus 로고
    • Closed geodesics on positively curved manifolds
    • W. Ballmann, G. Thobergsson, and W. Ziller, Closed geodesics on positively curved manifolds, Ann. of Math. 116 (1982), 213-247.
    • (1982) Ann. of Math. , vol.116 , pp. 213-247
    • Ballmann, W.1    Thobergsson, G.2    Ziller, W.3
  • 2
    • 84980073426 scopus 로고
    • On the iteration of closed geodesics and the Sturm intersection theory
    • R. Bott, On the iteration of closed geodesics and the Sturm intersection theory, Comm. Pure Appl. Math. 9 (1956), 171-206.
    • (1956) Comm. Pure Appl. Math. , vol.9 , pp. 171-206
    • Bott, R.1
  • 3
    • 0000278756 scopus 로고
    • L'index d'un système hamiltonien linéaire
    • V. Brousseau, L'index d'un système hamiltonien linéaire, C. R. Acad. Sci. Paris Ser. I 303 (1986), 351-354.
    • (1986) C. R. Acad. Sci. Paris Ser. I , vol.303 , pp. 351-354
    • Brousseau, V.1
  • 4
    • 84990569659 scopus 로고
    • Morse-type index theory for flows and periodic solutions for Hamiltonian equations
    • C. Conley and E. Zehnder, Morse-type index theory for flows and periodic solutions for Hamiltonian equations, Comm. Pure Appl. Math. 37 (1984), 207-253.
    • (1984) Comm. Pure Appl. Math. , vol.37 , pp. 207-253
    • Conley, C.1    Zehnder, E.2
  • 5
    • 0002019627 scopus 로고
    • The behavior of the index of a periodic linear Hamiltonian system under iteration
    • R. Cushman and J. J. Duistermaat, The behavior of the index of a periodic linear Hamiltonian system under iteration, Adv. Math. 23 (1977), 1-21.
    • (1977) Adv. Math. , vol.23 , pp. 1-21
    • Cushman, R.1    Duistermaat, J.J.2
  • 7
    • 0000741077 scopus 로고
    • Les systèmes hamiltoniens convexes et pairs ne sont pas ergodiques en général
    • G. Dell'Antoio, B. D'Onofrio, and I. Ekeland, Les systèmes hamiltoniens convexes et pairs ne sont pas ergodiques en général, C. R. Acad. Sci. Paris Ser. I 315 (1992), 1413-1415.
    • (1992) C. R. Acad. Sci. Paris Ser. I , vol.315 , pp. 1413-1415
    • Dell'Antoio, G.1    D'Onofrio, B.2    Ekeland, I.3
  • 8
    • 33646876246 scopus 로고    scopus 로고
    • The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems
    • D. Dong and Y. Long, The iteration formula of the Maslov-type index theory with applications to nonlinear Hamiltonian systems, Trans. Amer. Math. Soc. 349 (1997), 2619-2661.
    • (1997) Trans. Amer. Math. Soc. , vol.349 , pp. 2619-2661
    • Dong, D.1    Long, Y.2
  • 9
    • 38249020500 scopus 로고
    • Hamiltonian systems with elliptic periodic orbits
    • B. D'Onofrio and I. Ekeland, Hamiltonian systems with elliptic periodic orbits, Nonlinear Anal. 14 (1990), 11-21.
    • (1990) Nonlinear Anal. , vol.14 , pp. 11-21
    • D'Onofrio, B.1    Ekeland, I.2
  • 10
    • 0002250880 scopus 로고
    • A generalized Sturm theorem
    • H. M. Edwards, A generalized Sturm theorem, Ann. of Math. 80 (1964), 22-57.
    • (1964) Ann. of Math. , vol.80 , pp. 22-57
    • Edwards, H.M.1
  • 11
    • 84973997975 scopus 로고
    • Une théorie de Morse pour les systèmes hamiltoniens convexes
    • I. Ekeland, Une théorie de Morse pour les systèmes hamiltoniens convexes, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984), 19-78.
    • (1984) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.1 , pp. 19-78
    • Ekeland, I.1
  • 12
    • 0000529105 scopus 로고
    • An index theory for periodic solutions of convex Hamiltonian systems
    • "Nonlinear Funct. Anal. and Its Appl.," , Amer. Math. Soc., Providence
    • I. Ekeland, An index theory for periodic solutions of convex Hamiltonian systems, in "Nonlinear Funct. Anal. and Its Appl.," Proc. Sympos. Pure Math., Vol. 45, pp. 395-423, Amer. Math. Soc., Providence, 1986.
    • (1986) Proc. Sympos. Pure Math. , vol.45 , pp. 395-423
    • Ekeland, I.1
  • 14
    • 0000527973 scopus 로고
    • Convex Hamiltonian energy surfaces and their closed trajectories
    • I. Ekeland and H. Hofer, Convex Hamiltonian energy surfaces and their closed trajectories, Comm. Math. Phys. 113 (1987), 419-467.
    • (1987) Comm. Math. Phys. , vol.113 , pp. 419-467
    • Ekeland, I.1    Hofer, H.2
  • 15
    • 0002065640 scopus 로고
    • Multiplicité des trajectories formées d'un système hamiltonien sur une hypersurface d'énergie convexe
    • I. Ekeland and L. Lassoued, Multiplicité des trajectories formées d'un système hamiltonien sur une hypersurface d'énergie convexe, Ann. Inst. H. Poincaré Anal. Non Linéaire 4 (1987), 1-29.
    • (1987) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.4 , pp. 1-29
    • Ekeland, I.1    Lassoued, L.2
  • 16
    • 0001388207 scopus 로고
    • Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems
    • E. Fadell and P. Rabinowitz, Generalized cohomological index theories for Lie group actions with an application to bifurcation questions for Hamiltonian systems, Invent. Math. 45 (1978), 139-174.
    • (1978) Invent. Math. , vol.45 , pp. 139-174
    • Fadell, E.1    Rabinowitz, P.2
  • 17
    • 0002295140 scopus 로고
    • On the structure of the regions of stability of linear canonical systems of differential equations with periodic coefficients
    • In Russian
    • I. M. Gelfand and V. B. Lidskii, On the structure of the regions of stability of linear canonical systems of differential equations with periodic coefficients, Uspekhi Mat. Nauk 10 (1955), 3-40 [In Russian]; in Amer. Math. Soc. Transl. Ser. 2, Vol. 8, pp. 143-181, Amer. Math. Soc., Providence, 1958.
    • (1955) Uspekhi Mat. Nauk , vol.10 , pp. 3-40
    • Gelfand, I.M.1    Lidskii, V.B.2
  • 18
    • 0142245978 scopus 로고
    • Amer. Math. Soc., Providence
    • I. M. Gelfand and V. B. Lidskii, On the structure of the regions of stability of linear canonical systems of differential equations with periodic coefficients, Uspekhi Mat. Nauk 10 (1955), 3-40 [In Russian]; in Amer. Math. Soc. Transl. Ser. 2, Vol. 8, pp. 143-181, Amer. Math. Soc., Providence, 1958.
    • (1958) Amer. Math. Soc. Transl. Ser. 2 , vol.8 , pp. 143-181
  • 19
    • 0001968784 scopus 로고    scopus 로고
    • Normal forms of symplectic matrices. II
    • J. Han and Y. Long, Normal forms of symplectic matrices. II, Acta Sci. Nature Univ. Nankai 32(3) (1999), 30-41.
    • (1999) Acta Sci. Nature Univ. Nankai , vol.32 , Issue.3 , pp. 30-41
    • Han, J.1    Long, Y.2
  • 20
    • 0032352271 scopus 로고    scopus 로고
    • The dynamics on three-dimensional strictly convex energy surfaces
    • H. Hofer, K. Wysocki, and E. Zehnder, The dynamics on three-dimensional strictly convex energy surfaces, Ann. of Math. 148 (1998), 197-289.
    • (1998) Ann. of Math. , vol.148 , pp. 197-289
    • Hofer, H.1    Wysocki, K.2    Zehnder, E.3
  • 21
    • 0001745414 scopus 로고    scopus 로고
    • An optimal increasing estimate for Maslov-type indices of iterations
    • In Chinese
    • C. Liu and Y. Long, An optimal increasing estimate for Maslov-type indices of iterations, Chinese Sci. Bull. 42 (1997), 2275-2277 [In Chinese]; 43 (1998), 1063-1066. [In English]
    • (1997) Chinese Sci. Bull. , vol.42 , pp. 2275-2277
    • Liu, C.1    Long, Y.2
  • 22
    • 0000961315 scopus 로고    scopus 로고
    • In English
    • C. Liu and Y. Long, An optimal increasing estimate for Maslov-type indices of iterations, Chinese Sci. Bull. 42 (1997), 2275-2277 [In Chinese]; 43 (1998), 1063-1066. [In English]
    • (1998) Chinese Sci. Bull. , vol.43 , pp. 1063-1066
  • 23
    • 0002278962 scopus 로고    scopus 로고
    • Hyperbolic characteristics on star-shaped hypersurfaces
    • C. Liu and Y. Long, Hyperbolic characteristics on star-shaped hypersurfaces, Ann. Inst. H. Poincaré Anal. Non Linéaire 16 (1999), 725-746.
    • (1999) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.16 , pp. 725-746
    • Liu, C.1    Long, Y.2
  • 24
    • 0012536240 scopus 로고    scopus 로고
    • Iteration inequalities of the Maslov-type index theory with applications
    • preprint, Nankai University
    • C. Liu and Y. Long, Iteration inequalities of the Maslov-type index theory with applications, preprint, Nankai Inst. of Math., Nankai University, 1997, revised, 1998, J. Differential Equations, doi:10.1006/jdeq.2000.3775.
    • (1997) Nankai Inst. of Math.
    • Liu, C.1    Long, Y.2
  • 25
    • 0012536240 scopus 로고    scopus 로고
    • revised, doi:10.1006/jdeq.2000.3775
    • C. Liu and Y. Long, Iteration inequalities of the Maslov-type index theory with applications, preprint, Nankai Inst. of Math., Nankai University, 1997, revised, 1998, J. Differential Equations, doi:10.1006/jdeq.2000.3775.
    • (1998) J. Differential Equations
  • 26
    • 0001630227 scopus 로고
    • Maslov-type index, degenerate critical points, and asymptotically linear Hamiltonian systems
    • In Chinese
    • Y. Long, Maslov-type index, degenerate critical points, and asymptotically linear Hamiltonian systems, Sci. China Ser. A 7 (1990), 673-682 [In Chinese]; 33(1990), 1409-1419. [In English]
    • (1990) Sci. China Ser. A , vol.7 , pp. 673-682
    • Long, Y.1
  • 27
    • 0001630228 scopus 로고
    • In English
    • Y. Long, Maslov-type index, degenerate critical points, and asymptotically linear Hamiltonian systems, Sci. China Ser. A 7 (1990), 673-682 [In Chinese]; 33(1990), 1409-1419. [In English]
    • (1990) Sci. China Ser. A , vol.33 , pp. 1409-1419
  • 28
    • 0000513190 scopus 로고
    • The structure of the singular symplectic matrix set
    • In Chinese
    • Y. Long, The structure of the singular symplectic matrix set, Sci. China Ser. A 5 (1991), 457-465 [In Chinese]; 34 (1991), 897-907. [In English]
    • (1991) Sci. China Ser. A , vol.5 , pp. 457-465
    • Long, Y.1
  • 29
    • 0347060944 scopus 로고
    • In English
    • Y. Long, The structure of the singular symplectic matrix set, Sci. China Ser. A 5 (1991), 457-465 [In Chinese]; 34 (1991), 897-907. [In English]
    • (1991) Sci. China Ser. A , vol.34 , pp. 897-907
  • 30
    • 0001043584 scopus 로고
    • Maslov-type index theory and asymptotically linear Hamiltonian systems
    • (K. Shiraiwa, Ed.), World Scientific, Singapore
    • Y. Long, Maslov-type index theory and asymptotically linear Hamiltonian systems, in "Dyna. Syst. and Rel. Topics" (K. Shiraiwa, Ed.), pp. 333-341, World Scientific, Singapore, 1991.
    • (1991) Dyna. Syst. and Rel. Topics , pp. 333-341
    • Long, Y.1
  • 32
    • 85012273335 scopus 로고
    • The minimal period problem for classical Hamiltonian systems with even potentials
    • Y. Long, The minimal period problem for classical Hamiltonian systems with even potentials, Ann. Inst. H. Poincaré Anal. Non Linéaire 10 (1993), 605-626.
    • (1993) Ann. Inst. H. Poincaré Anal. Non Linéaire , vol.10 , pp. 605-626
    • Long, Y.1
  • 33
    • 33646889177 scopus 로고
    • The minimal period problem of periodic solutions for autonomous super-quadratic second order Hamiltonian systems
    • Y. Long, The minimal period problem of periodic solutions for autonomous super-quadratic second order Hamiltonian systems, J. Differential Equations 111 (1994), 147-174.
    • (1994) J. Differential Equations , vol.111 , pp. 147-174
    • Long, Y.1
  • 35
    • 0003166967 scopus 로고    scopus 로고
    • A Maslov-type index theory for symplectic paths
    • Y. Long, A Maslov-type index theory for symplectic paths, Topol. Methods Nonlinear Anal. 10 (1997), 47-78.
    • (1997) Topol. Methods Nonlinear Anal. , vol.10 , pp. 47-78
    • Long, Y.1
  • 37
    • 0001496478 scopus 로고    scopus 로고
    • Bott formula of the Maslov-type index theory
    • Y. Long, Bott formula of the Maslov-type index theory, Pacific J. Math. 187 (1999), 113-149.
    • (1999) Pacific J. Math. , vol.187 , pp. 113-149
    • Long, Y.1
  • 38
    • 0000381063 scopus 로고    scopus 로고
    • The topological structures of ω-subsets of symplectic groups
    • Y. Long, The topological structures of ω-subsets of symplectic groups, Acta Math. Sinica 15 (1999), 255-268.
    • (1999) Acta Math. Sinica , vol.15 , pp. 255-268
    • Long, Y.1
  • 39
    • 0034347313 scopus 로고    scopus 로고
    • Multiple periodic points of the Poincaré map of Lagrangian systems on tori
    • Y. Long, Multiple periodic points of the Poincaré map of Lagrangian systems on tori, Math. Z. 233 (2000), 443-470.
    • (2000) Math. Z. , vol.233 , pp. 443-470
    • Long, Y.1
  • 40
    • 21944450086 scopus 로고    scopus 로고
    • On the minimal period for periodic solutions of nonlinear Hamiltonian systems
    • Y. Long, On the minimal period for periodic solutions of nonlinear Hamiltonian systems, Chinese Ann. Math. Ser. B 18 (1997), 481-485.
    • (1997) Chinese Ann. Math. Ser. B , vol.18 , pp. 481-485
    • Long, Y.1
  • 41
    • 0002091012 scopus 로고    scopus 로고
    • The Maslov-type index and its iteration theory with applications to Hamiltonian systems
    • Third School on Nonlinear Analysis and Applications to Differential Equations 10.12-20, ICTP Lecture Notes, SMR 1071/2, in press
    • Y. Long, The Maslov-type index and its iteration theory with applications to Hamiltonian systems, Third School on Nonlinear Analysis and Applications to Differential Equations (10.12-20, 1998), ICTP Lecture Notes, SMR 1071/2, Proc. Inst. Math. Acad. Sinica., in press.
    • (1998) Proc. Inst. Math. Acad. Sinica.
    • Long, Y.1
  • 42
    • 0000850691 scopus 로고    scopus 로고
    • Indexing the domains of instability for Hamiltonian systems
    • Y. Long and T. An, Indexing the domains of instability for Hamiltonian systems, NoDEA Nonlinear Differential Equations Appl. 5 (1998), 461-478.
    • (1998) NoDEA Nonlinear Differential Equations Appl. , vol.5 , pp. 461-478
    • Long, Y.1    An, T.2
  • 43
    • 0002103784 scopus 로고
    • Normal forms of symplectic matrices
    • preprint, Nankai University
    • Y. Long and D. Dong, Normal forms of symplectic matrices, preprint, Nankai Inst. of Math., Nankai University, 1995; Acta Math. Sinica, in press.
    • (1995) Nankai Inst. of Math.
    • Long, Y.1    Dong, D.2
  • 44
    • 85031548513 scopus 로고    scopus 로고
    • in press
    • Y. Long and D. Dong, Normal forms of symplectic matrices, preprint, Nankai Inst. of Math., Nankai University, 1995; Acta Math. Sinica, in press.
    • Acta Math. Sinica
  • 45
    • 0002182215 scopus 로고
    • Morse theory for forced oscillations of asymptotically linear Hamiltonian systems
    • (S. Albeverio et al., Eds.), World Scientific, Singapore
    • Y. Long and E. Zehnder, Morse theory for forced oscillations of asymptotically linear Hamiltonian systems, in "Stoc. Proc. Phys. and Geom." (S. Albeverio et al., Eds.), pp. 528-563, World Scientific, Singapore, 1990.
    • (1990) Stoc. Proc. Phys. and Geom. , pp. 528-563
    • Long, Y.1    Zehnder, E.2
  • 46
    • 0034387275 scopus 로고    scopus 로고
    • Maslov-type index theory for symplectic paths and spectral flow, II
    • Y. Long and C. Zhu, Maslov-type index theory for symplectic paths and spectral flow, II, Chinese Ann. Math. Ser. B 21, 1 (2000), 89-108.
    • (2000) Chinese Ann. Math. Ser. B , vol.21 , Issue.1 , pp. 89-108
    • Long, Y.1    Zhu, C.2
  • 47
    • 84980072725 scopus 로고
    • New aspects in the theory of stability of Hamiltonian systems
    • J. K. Moser, New aspects in the theory of stability of Hamiltonian systems, Comm. Pure Appl. Math. 11 (1958), 81-114.
    • (1958) Comm. Pure Appl. Math. , vol.11 , pp. 81-114
    • Moser, J.K.1
  • 48
    • 84980196930 scopus 로고
    • Periodic solutions of Hamiltonian systems
    • P. Rabinowitz, Periodic solutions of Hamiltonian systems, Comm. Pure Appl. Math. 31 (1978), 157-184.
    • (1978) Comm. Pure Appl. Math. , vol.31 , pp. 157-184
    • Rabinowitz, P.1
  • 49
    • 84972538152 scopus 로고
    • On the average indices of closed geodesics
    • H.-B. Rademacher, On the average indices of closed geodesics, J. Diff. Geom. 29 (1989), 65-83.
    • (1989) J. Diff. Geom. , vol.29 , pp. 65-83
    • Rademacher, H.-B.1
  • 50
    • 84990617874 scopus 로고
    • Morse theory for periodic solutions of Hamiltonian systems and the Maslov index
    • D. Salamon and E. Zehnder, Morse theory for periodic solutions of Hamiltonian systems and the Maslov index, Comm. Pure Appl. Math. 45 (1992), 1303-1360.
    • (1992) Comm. Pure Appl. Math. , vol.45 , pp. 1303-1360
    • Salamon, D.1    Zehnder, E.2
  • 51
    • 0001671576 scopus 로고
    • Morse theory and existence of periodic solutions of convex Hamiltonian systems
    • A. Szulkin, Morse theory and existence of periodic solutions of convex Hamiltonian systems, Bull. Soc. Math. France (1987).
    • (1987) Bull. Soc. Math. France
    • Szulkin, A.1
  • 52
    • 0002372214 scopus 로고
    • Equivariant Morse theory for starshaped Hamiltonian systems
    • C. Viterbo, Equivariant Morse theory for starshaped Hamiltonian systems, Trans. Amer. Math. Soc. 311 (1989), 621-655.
    • (1989) Trans. Amer. Math. Soc. , vol.311 , pp. 621-655
    • Viterbo, C.1
  • 53
    • 0001776080 scopus 로고
    • A new obstruction to embedding Lagrangian tori
    • C. Viterbo, A new obstruction to embedding Lagrangian tori, Invent. Math. 100 (1990), 301-320.
    • (1990) Invent. Math. , vol.100 , pp. 301-320
    • Viterbo, C.1
  • 54
    • 0001251052 scopus 로고
    • Periodic orbits for convex Hamiltonian systems
    • A. Weinstein, Periodic orbits for convex Hamiltonian systems, Ann. of Math. 108 (1978), 507-518.
    • (1978) Ann. of Math. , vol.108 , pp. 507-518
    • Weinstein, A.1
  • 56
    • 0033476188 scopus 로고    scopus 로고
    • Maslov-type index theory for symplectic paths and spectral flow, I
    • C. Zhu and Y. Long, Maslov-type index theory for symplectic paths and spectral flow, I, Chinese Ann. Math. 208 (1999), 413-424.
    • (1999) Chinese Ann. Math. , vol.208 , pp. 413-424
    • Zhu, C.1    Long, Y.2


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