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Volumn 54, Issue 3, 2003, Pages 484-502

Rotation number for non-autonomous linear Hamiltonian systems I: Basic properties

Author keywords

Hamiltonian system; Rotation number; Symplectic geometry

Indexed keywords


EID: 0038508936     PISSN: 00442275     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00033-003-1068-1     Document Type: Article
Times cited : (37)

References (36)
  • 1
    • 0009153436 scopus 로고
    • A multiplicative ergodic theorem for rotation numbers
    • L. Arnold, L. San Martin, A multiplicative ergodic theorem for rotation numbers, J. Dynam. Differential Equations 1(1) (1989), 95-119.
    • (1989) J. Dynam. Differential Equations , vol.1 , Issue.1 , pp. 95-119
    • Arnold, L.1    San Martin, L.2
  • 2
    • 33646925958 scopus 로고
    • On a characteristic class entering in a quantum condition
    • V.I. Arnold, On a characteristic class entering in a quantum condition, Func. Anal. Appl. 1 (1967), 1-14.
    • (1967) Func. Anal. Appl. , vol.1 , pp. 1-14
    • Arnold, V.I.1
  • 3
    • 0000557265 scopus 로고
    • The Sturm theorems and symplectic geometry
    • V.I. Arnold, The Sturm theorems and symplectic geometry, Func. Anal. Appl. 19 (1985), 251-259.
    • (1985) Func. Anal. Appl. , vol.19 , pp. 251-259
    • Arnold, V.I.1
  • 4
    • 84968511130 scopus 로고
    • A Prüfer transformation for matrix differential equations
    • J.H. Barret, A Prüfer transformation for matrix differential equations, Proc. Amer. Math. Soc. 8 (1957), 510-518.
    • (1957) Proc. Amer. Math. Soc. , vol.8 , pp. 510-518
    • Barret, J.H.1
  • 5
    • 84980073426 scopus 로고
    • On the iteration of closed geodesic and the Sturm intersection theory
    • R. Bott, On the iteration of closed geodesic and the Sturm intersection theory. Commun. Pure and Applied Math. 9 (2) (1956), 171-206.
    • (1956) Commun. Pure and Applied Math. , vol.9 , Issue.2 , pp. 171-206
    • Bott, R.1
  • 7
    • 0001329024 scopus 로고
    • On the Morse index in variational calculus
    • J.J. Duistermaat, On the Morse index in variational calculus, Adv. Math. 21 (1976), 173-195.
    • (1976) Adv. Math. , vol.21 , pp. 173-195
    • Duistermaat, J.J.1
  • 8
    • 0038508936 scopus 로고    scopus 로고
    • Rotation number for non-autonomous linear Hamiltonian systems II: The Floquet exponent
    • R. Fabbri, R. Johnson, C. Ńñez, Rotation number for non-autonomous linear Hamiltonian systems II: The Floquet exponent, Z. angew. Math. Phys. 54 (2003).
    • (2003) Z. Angew. Math. Phys. , vol.54
    • Fabbri, R.1    Johnson, R.2    Ńñez, C.3
  • 9
    • 0037512393 scopus 로고    scopus 로고
    • On the Yakubovich frequency theorem for non-autonomous control processes
    • R. Fabbri, R. Johnson, C. Núñez, On the Yakubovich frequency theorem for non-autonomous control processes, Diser. Cont. Dyr. Sys. 9(3) (2003), 677-704.
    • (2003) Diser. Cont. Dyr. Sys. , vol.9 , Issue.3 , pp. 677-704
    • Fabbri, R.1    Johnson, R.2    Núñez, C.3
  • 11
    • 0000366176 scopus 로고
    • On the structure of the regions of stability of linear canonical systems of differential equations with periodic coefficients
    • I.M. Gel'fand, V.B. Lidskiǐ, On the structure of the regions of stability of linear canonical systems of differential equations with periodic coefficients, Amer. Mat. Soc. Transl. (2) 8 (1958), 143-181.
    • (1958) Amer. Mat. Soc. Transl. (2) , vol.8 , pp. 143-181
    • Gel'fand, I.M.1    Lidskiǐ, V.B.2
  • 13
    • 0001441740 scopus 로고
    • Invariant manifolds
    • Springer-Verlag, Berlin, Heidelberg, New York
    • W.M. Hirsch, C.C. Pugh, M. Shub, Invariant manifolds, Lecture Notes in Math. 583, Springer-Verlag, Berlin, Heidelberg, New York, 1977.
    • (1977) Lecture Notes in Math. , vol.583
    • Hirsch, W.M.1    Pugh, C.C.2    Shub, M.3
  • 14
    • 0037534540 scopus 로고
    • Exponential dichotomy, rotation number, and linear differential operators with bounded coefficients
    • R. Johnson, Exponential dichotomy, rotation number, and linear differential operators with bounded coefficients, J. Differential Equations 61 (1986), 54-78.
    • (1986) J. Differential Equations , vol.61 , pp. 54-78
    • Johnson, R.1
  • 15
    • 0000809966 scopus 로고
    • m-functions and Floquet exponents for linear differential systems
    • R. Johnson, m-functions and Floquet exponents for linear differential systems, Ann. Mat. Pura Appl. 147 (1987), 211-248.
    • (1987) Ann. Mat. Pura Appl. , vol.147 , pp. 211-248
    • Johnson, R.1
  • 16
    • 0000423029 scopus 로고
    • The rotation number for almost periodic differential equations
    • R. Johnson, J. Moser, The rotation number for almost periodic differential equations, Comm. Math. Phys. 84 (1982), 403-438.
    • (1982) Comm. Math. Phys. , vol.84 , pp. 403-438
    • Johnson, R.1    Moser, J.2
  • 17
    • 0000098357 scopus 로고
    • Exponential dichotomy and rotation number for linear Hamiltonian systems
    • R. Johnson, M. Nerurkar, Exponential dichotomy and rotation number for linear Hamiltonian systems, J. Differential Equations 108 (1994), 201-216.
    • (1994) J. Differential Equations , vol.108 , pp. 201-216
    • Johnson, R.1    Nerurkar, M.2
  • 18
    • 0029684697 scopus 로고    scopus 로고
    • Stabilization and random linear regulator problem for random linear control processes
    • R. Johnson, M. Nerurkar, Stabilization and random linear regulator problem for random linear control processes, J. Math. Anal. Appl. 197 (1996), 608-629.
    • (1996) J. Math. Anal. Appl. , vol.197 , pp. 608-629
    • Johnson, R.1    Nerurkar, M.2
  • 19
    • 33748820691 scopus 로고    scopus 로고
    • Controllability, stabilization, and the regulator problem for random differential systems
    • Amer. Math. Soc., Providence
    • R. Johnson, M. Nerurkar, Controllability, stabilization, and the regulator problem for random differential systems, Mem. Amer. Math. Soc. 646, Amer. Math. Soc., Providence, 1998.
    • (1998) Mem. Amer. Math. Soc. , vol.646
    • Johnson, R.1    Nerurkar, M.2
  • 20
    • 0001848182 scopus 로고
    • Lyapunov indices determine absolutely continuous spectrum of stationary random 1-dimensional Schrödinger equations
    • S.A.Katata
    • S. Kotani, Lyapunov indices determine absolutely continuous spectrum of stationary random 1-dimensional Schrödinger equations, Proc. of Taniguchi Sympos., S.A.Katata (1982), 225-247.
    • (1982) Proc. of Taniguchi Sympos. , pp. 225-247
    • Kotani, S.1
  • 23
    • 0004500735 scopus 로고    scopus 로고
    • Ergodic properties and rotation number for linear Hamiltonian systems
    • S. Novo, C. Núñez, R. Obaya, Ergodic properties and rotation number for linear Hamiltonian systems, J. Differential Equations 148 (1998), 148-185.
    • (1998) J. Differential Equations , vol.148 , pp. 148-185
    • Novo, S.1    Núñez, C.2    Obaya, R.3
  • 24
    • 0001261668 scopus 로고
    • Exponential dichotomies, the shadowing-lemma and transversal homoclinic points
    • K.J. Palmer, Exponential dichotomies, the shadowing-lemma and transversal homoclinic points, Dynam. Report. 1 (1988), 265-306.
    • (1988) Dynam. Report. , vol.1 , pp. 265-306
    • Palmer, K.J.1
  • 26
    • 84972545013 scopus 로고
    • A Prüfer transformation for differential systems
    • W.T. Reid, A Prüfer transformation for differential systems, Pac. J. Math. 8 (1958), 575-584.
    • (1958) Pac. J. Math. , vol.8 , pp. 575-584
    • Reid, W.T.1
  • 27
    • 0004536821 scopus 로고
    • Sturmian theory for ordinary differential equations
    • Springer-Verlag, New York
    • W.T. Reid, Sturmian Theory for Ordinary Differential Equations, Applied Mathematical Sciences 31, Springer-Verlag, New York, 1980.
    • (1980) Applied Mathematical Sciences , vol.31
    • Reid, W.T.1
  • 28
  • 29
    • 49349126301 scopus 로고
    • A spectral theory for linear differential systems
    • R.J. Sacker, G.R. Sell, A spectral theory for linear differential systems, J. Differential Equations 27 (1978), 320-358.
    • (1978) J. Differential Equations , vol.27 , pp. 320-358
    • Sacker, R.J.1    Sell, G.R.2
  • 30
    • 0000720459 scopus 로고
    • Asymptotic cycles
    • S. Schwarzmann, Asymptotic cycles, Ann. Math. 66 (2) (1957), 270-284.
    • (1957) Ann. Math. , vol.66 , Issue.2 , pp. 270-284
    • Schwarzmann, S.1
  • 31
    • 0038061159 scopus 로고
    • Arguments on the group of symplectic matrices
    • Russian
    • V.A. Yakubovich, Arguments on the group of symplectic matrices, Mat. Sb. 55 (97) (1961), 255-280 (Russian).
    • (1961) Mat. Sb. , vol.55 , Issue.97 , pp. 255-280
    • Yakubovich, V.A.1
  • 32
    • 0038737568 scopus 로고
    • Oscillatory properties of the solutions of canonical equations
    • V.A. Yakubovich, Oscillatory properties of the solutions of canonical equations, Amer. Math. Soc. Transl. Ser. 2 42 (1964), 247-288.
    • (1964) Amer. Math. Soc. Transl. Ser. 2 , vol.42 , pp. 247-288
    • Yakubovich, V.A.1
  • 33
    • 0038399438 scopus 로고
    • A linear-quadratic optimization problem and the frequency theorem for periodic systems I
    • V.A. Yakubovich, A linear-quadratic optimization problem and the frequency theorem for periodic systems I, Siberian Math. J. 27 (4) (1986), 614-630.
    • (1986) Siberian Math. J. , vol.27 , Issue.4 , pp. 614-630
    • Yakubovich, V.A.1
  • 34
    • 0037723534 scopus 로고
    • Linear-quadratic optimization problem and the frequency theorem for periodic systems II
    • V.A. Yakubovich, Linear-quadratic optimization problem and the frequency theorem for periodic systems II, Siberian Math. J. 31 (6) (1990), 1027-1039.
    • (1990) Siberian Math. J. , vol.31 , Issue.6 , pp. 1027-1039
    • Yakubovich, V.A.1
  • 36
    • 0001731171 scopus 로고
    • A generalized integral manifold theorem
    • Y. Yi, A generalized integral manifold theorem, J. Differential Equations 102 (1993), 153-187.
    • (1993) J. Differential Equations , vol.102 , pp. 153-187
    • Yi, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.