-
1
-
-
0001283157
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
-
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
-
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
-
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
-
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
-
-
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
-
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
-
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
-
-
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
-
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
-
-
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
-
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
-
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
-
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
|