메뉴 건너뛰기




Volumn 19, Issue 6, 2006, Pages 1415-1445

The inner equation for one and a half degrees of freedom rapidly forced Hamiltonian systems

Author keywords

[No Author keywords available]

Indexed keywords


EID: 33646724250     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/19/6/011     Document Type: Article
Times cited : (22)

References (27)
  • 1
    • 0002157395 scopus 로고
    • A variational interpretation of Melnikov's function and exponentially small separatrix splitting
    • Angenent S 1993 A variational interpretation of Melnikov's function and exponentially small separatrix splitting Symplectic Geometry (London Math. Soc. Lecture Note Ser. vol 192) (Cambridge: Cambridge University Press) pp 5-35
    • (1993) Symplectic Geometry , pp. 5-35
    • Angenent, S.1
  • 2
    • 0000877933 scopus 로고
    • Instability of dynamical systems with many degrees of freedom
    • 0197-6788
    • Arnold V I 1964 Instability of dynamical systems with many degrees of freedom Sov. Math.-Dokl. 5 581-5
    • (1964) Sov. Math.-Dokl. , vol.5 , pp. 581-585
    • Arnold, V.I.1
  • 3
    • 0742285264 scopus 로고    scopus 로고
    • Exponentially small splitting of invariant manifolds of parabolic points
    • Baldom I and Fontich E 2004 Exponentially small splitting of invariant manifolds of parabolic points Memoirs of AMS vol 167 (792) p x+83
    • (2004) Memoirs of AMS , vol.167 , Issue.792 , pp. 83
    • Baldom, I.1    Fontich, E.2
  • 4
    • 0032394646 scopus 로고    scopus 로고
    • Adiabatic invariant of the harmonic oscillator, complex matching and resurgence methods
    • 10.1137/S0036141097321516 0036-1410
    • Bonet C, Sauzin D, Seara T M and València M 1998 Adiabatic invariant of the harmonic oscillator, complex matching and resurgence methods SIAM J. Math. Anal. 29 1335-60
    • (1998) SIAM J. Math. Anal. , vol.29 , Issue.6 , pp. 1335-1360
    • Bonet, C.1    Sauzin, D.2    Seara, T.M.3    València, M.4
  • 6
    • 0000467096 scopus 로고    scopus 로고
    • Exponentially small splitting of separatrices for perturbed integrable standard-like maps
    • 10.1007/s003329900054 0938-8974
    • Delshams A and Ramírez-Ros R 1998 Exponentially small splitting of separatrices for perturbed integrable standard-like maps J. Nonlinear Sci. 8 317-52
    • (1998) J. Nonlinear Sci. , vol.8 , Issue.3 , pp. 317-352
    • Delshams, A.1    Ramírez-Ros, R.2
  • 7
    • 21144460556 scopus 로고
    • An asymptotic expression for the splitting of separatrices of the rapidly forced pendulum
    • 10.1007/BF02096956 0010-3616
    • Delshams A and Seara T M 1992 An asymptotic expression for the splitting of separatrices of the rapidly forced pendulum Commun. Math. Phys. 150 433-63
    • (1992) Commun. Math. Phys. , vol.150 , Issue.3 , pp. 433-463
    • Delshams, A.1    Seara, T.M.2
  • 8
    • 0041485922 scopus 로고    scopus 로고
    • Splitting of separatrices in Hamiltonian systems with one and a half degrees of freedom
    • 1086-6655
    • Delshams A and Seara T M 1997 Splitting of separatrices in Hamiltonian systems with one and a half degrees of freedom Math. Phys. Electron. J. 3 4-40
    • (1997) Math. Phys. Electron. J. , vol.3 , pp. 4-40
    • Delshams, A.1    Seara, T.M.2
  • 9
    • 0039933214 scopus 로고
    • Les fonctions résurgentes
    • calle J 1981 Les fonctions résurgentes Publ. Math. d'Orsay vol 1 81-05
    • (1981) Publ. Math. d'Orsay , vol.1 , pp. 81-05
    • Calle, J.1
  • 10
    • 0039933214 scopus 로고
    • Les fonctions résurgentes
    • calle J 1981 Les fonctions résurgentes Publ. Math. d'Orsay vol 2 81-06
    • (1981) Publ. Math. d'Orsay , vol.2 , pp. 81-06
    • Calle, J.1
  • 11
    • 0039933214 scopus 로고
    • Les fonctions résurgentes
    • calle J 1985 Les fonctions résurgentes Publ. Math. d'Orsay vol 3 85-05
    • (1985) Publ. Math. d'Orsay , vol.3 , pp. 85-05
    • Calle, J.1
  • 12
    • 0000862628 scopus 로고
    • Exponentially small upper bounds for the splitting of separatrices for high frequency periodic perturbations
    • 10.1016/0362-546X(93)90031-M 0362-546X
    • Fontich F 1993 Exponentially small upper bounds for the splitting of separatrices for high frequency periodic perturbations Nonlinear Anal. 20 733-44
    • (1993) Nonlinear Anal. , vol.20 , Issue.6 , pp. 733-744
    • Fontich, F.1
  • 13
    • 0000996835 scopus 로고
    • Rapidly forced planar vector fields and splitting of separatrices
    • 10.1006/jdeq.1995.1093 0022-0396
    • Fontich F 1995 Rapidly forced planar vector fields and splitting of separatrices J. Diff. Eqns 119 310-35
    • (1995) J. Diff. Eqns , vol.119 , Issue.2 , pp. 310-335
    • Fontich, F.1
  • 14
    • 84971996008 scopus 로고
    • The splitting of separatrices for analytic diffeomorphisms
    • Fontich F and Sim C 1990 The splitting of separatrices for analytic diffeomorphisms Ergod. Theory Dynam. Syst. 10 295-318
    • (1990) Ergod. Theory Dynam. Syst. , vol.10 , pp. 295-318
    • Fontich, F.1    Sim, C.2
  • 15
    • 0000664107 scopus 로고    scopus 로고
    • Melnikov method and exponentially small splitting of separatrices
    • 10.1016/S0167-2789(96)00133-9 0167-2789 D
    • Gelfreich V G 1997 Melnikov method and exponentially small splitting of separatrices Physica D 101 227-48
    • (1997) Physica , vol.101 , Issue.3-4 , pp. 227-248
    • Gelfreich, V.G.1
  • 16
    • 0033241455 scopus 로고    scopus 로고
    • A proof of the exponentially small transversality of the separatrices for the standard map
    • 10.1007/s002200050553 0010-3616
    • Gelfreich V G 1999 A proof of the exponentially small transversality of the separatrices for the standard map Commun. Math. Phys. 201 155-216
    • (1999) Commun. Math. Phys. , vol.201 , Issue.1 , pp. 155-216
    • Gelfreich, V.G.1
  • 17
    • 0035612003 scopus 로고    scopus 로고
    • Borel summation and splitting of separatrices for the Hénon map
    • Gelfreich V G and Sauzin D 2001 Borel summation and splitting of separatrices for the Hénon map Ann. Inst. Fourier Grenoble 51 1001-55
    • (2001) Ann. Inst. Fourier Grenoble , vol.51 , pp. 1001-1055
    • Gelfreich, V.G.1    Sauzin, D.2
  • 18
    • 0000255261 scopus 로고
    • Exponentially small splitting of separatrices with applications to KAM theory and degenerate bifurcations
    • Holmes P, Marsden J and Scheurle J 1988 Exponentially small splitting of separatrices with applications to KAM theory and degenerate bifurcations Contemp. Math. 81 213-44
    • (1988) Contemp. Math. , vol.81 , pp. 213-244
    • Holmes, P.1    Marsden, J.2    Scheurle, J.3
  • 20
    • 0001834849 scopus 로고
    • On the stability of the center for time periodic perturbations
    • Melnikov V F 1963 On the stability of the center for time periodic perturbations Trans. Moscow Math. Soc. 12 3-56
    • (1963) Trans. Moscow Math. Soc. , vol.12 , pp. 3-56
    • Melnikov, V.F.1
  • 21
    • 1642336331 scopus 로고    scopus 로고
    • Matching complejo y resurgencia en el problema de la escisin de separatrices
    • Olivé C and Seara T M 1999 Matching complejo y resurgencia en el problema de la escisin de separatrices Actas CEDYA99 419-26
    • (1999) Actas CEDYA99 , pp. 419-426
    • Olivé, C.1    Seara, T.M.2
  • 23
    • 77951516344 scopus 로고
    • Sur le problème des trois corps et les équations de la dynamique
    • 0001-5962
    • Poincaré H 1890 Sur le problème des trois corps et les équations de la dynamique Acta Math. 13 1-271
    • (1890) Acta Math. , vol.13 , pp. 1-271
    • Poincaré, H.1
  • 24
    • 0001350288 scopus 로고
    • Résurgence paramétrique et exponentielle petitesse de l'écart des séparatrices du pendule rapidement forcé
    • Sauzin D 1995 Résurgence paramétrique et exponentielle petitesse de l'écart des séparatrices du pendule rapidement forcé Ann. Inst. Fourier, Grenoble 45 453-511
    • (1995) Ann. Inst. Fourier, Grenoble , vol.45 , pp. 453-511
    • Sauzin, D.1
  • 25
    • 0007322108 scopus 로고    scopus 로고
    • A new method for measuring the splitting of invariant manifolds
    • Sauzin D 2001 A new method for measuring the splitting of invariant manifolds Ann. Scient. c. Norm. Sup. 4 159-221
    • (2001) Ann. Scient. C. Norm. Sup. , vol.4 , pp. 159-221
    • Sauzin, D.1
  • 26
    • 0000615478 scopus 로고
    • Exponentially small estimates for separatrix splitting
    • Scheurle J, Marsden J and Holmes P 1991 Exponentially small estimates for separatrix splitting Asymptotics Beyond All Orders (La Jolla, CA, 1991) (NATO Adv. Sci. Inst. Ser. B Phys. vol 284) (New York: Plenum) pp 187-95
    • (1991) Asymptotics beyond All Orders , pp. 187-195
    • Scheurle, J.1    Marsden, J.2    Holmes, P.3
  • 27
    • 0031312703 scopus 로고    scopus 로고
    • Separatrix splitting for a pendulum with rapidly oscillating suspension point
    • 1061-9208
    • Treschev D V 1997 Separatrix splitting for a pendulum with rapidly oscillating suspension point Russ. J. Math. Phys. 5 63-98
    • (1997) Russ. J. Math. Phys. , vol.5 , pp. 63-98
    • Treschev, D.V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.