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Volumn 11, Issue 4, 2004, Pages 785-826

Exponentially small splitting for whiskered tori in Hamiltonian systems: Flow-box coordinates and upper bounds

Author keywords

Flow box coordinates; Hyperbolic KAM theory; Poincar Melnikov method

Indexed keywords


EID: 4644348564     PISSN: 10780947     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcds.2004.11.785     Document Type: Article
Times cited : (15)

References (24)
  • 1
    • 0000877933 scopus 로고
    • Instability of dynamical systems with several degrees of freedom
    • [Arn64]
    • [Arn64] V.I. Arnold. Instability of dynamical systems with several degrees of freedom. Soviet Math. Dokl., 5(3):581-585, 1964.
    • (1964) Soviet Math. Dokl. , vol.5 , Issue.3 , pp. 581-585
    • Arnold, V.I.1
  • 2
    • 0030187305 scopus 로고    scopus 로고
    • Effective stability and KAM theory
    • [DG96]
    • [DG96] A. Delshams and P. Gutiérrez. Effective stability and KAM theory. J. Differential Equations, 128(2):415-490, 1996.
    • (1996) J. Differential Equations , vol.128 , Issue.2 , pp. 415-490
    • Delshams, A.1    Gutiérrez, P.2
  • 3
    • 0013256095 scopus 로고    scopus 로고
    • Splitting potential and the Poincaré-Melnikov method for whiskered tori in Hamiltonian systems
    • [DG00]
    • [DG00] A. Delshams and P. Gutiérrez. Splitting potential and the Poincaré-Melnikov method for whiskered tori in Hamiltonian systems. J. Nonlinear Sci., 10(4):433-476, 2000.
    • (2000) J. Nonlinear Sci. , vol.10 , Issue.4 , pp. 433-476
    • Delshams, A.1    Gutiérrez, P.2
  • 4
    • 13244254241 scopus 로고    scopus 로고
    • Homoclinic orbits to invariant tori in Hamiltonian systems
    • [DG01] C.K.R.T. Jones and A.I. Khibnik, editors. Held in Minneapolis, 27-31 October, 1997. Springer-Verlag, New York
    • [DG01] A. Delshams and P. Gutiérrez. Homoclinic orbits to invariant tori in Hamiltonian systems. In C.K.R.T. Jones and A.I. Khibnik, editors, Multiple-Time-Scale Dynamical Systems, volume 122 of IMA Vol. Math. Appl., pages 1-27. Held in Minneapolis, 27-31 October, 1997. Springer-Verlag, New York, 2001.
    • (2001) Multiple-time-scale Dynamical Systems, Volume 122 of IMA Vol. Math. Appl. , vol.122 , pp. 1-27
    • Delshams, A.1    Gutiérrez, P.2
  • 5
    • 13244296805 scopus 로고    scopus 로고
    • Exponentially small splitting for whiskered tori in Hamiltonian systems: Continuation of transverse homoclinic orbits
    • [DG04]
    • [DG04] A. Delshams and P. Gutiérrez. Exponentially small splitting for whiskered tori in Hamiltonian systems: Continuation of transverse homoclinic orbits. Discrete Contin. Dynam. Systems, 11(4):757-783, 2004.
    • (2004) Discrete Contin. Dynam. Systems , vol.11 , Issue.4 , pp. 757-783
    • Delshams, A.1    Gutiérrez, P.2
  • 6
    • 0031494862 scopus 로고    scopus 로고
    • Exponentially small splitting of separatrices under fast quasiperiodic forcing
    • [DGJS97]
    • [DGJS97] A. Delshams, V.G. Gelfreich, À. Jorba, and T.M. Seara. Exponentially small splitting of separatrices under fast quasiperiodic forcing. Comm. Math. Phys., 189:35-71, 1997.
    • (1997) Comm. Math. Phys. , vol.189 , pp. 35-71
    • Delshams, A.1    Gelfreich, V.G.2    Jorba, À.3    Seara, T.M.4
  • 7
    • 0000467096 scopus 로고    scopus 로고
    • Exponentially small splitting of separatrices for perturbed integrable standard-like maps
    • [DR98]
    • [DR98] A. Delshams and R. Ramírez-Ros. Exponentially small splitting of separatrices for perturbed integrable standard-like maps. J. Nonlinear Sci., 8(3):317-352, 1998.
    • (1998) J. Nonlinear Sci. , vol.8 , Issue.3 , pp. 317-352
    • Delshams, A.1    Ramírez-Ros, R.2
  • 8
    • 21144460556 scopus 로고
    • An asymptotic expression for the splitting of separatrices of the rapidly forced pendulum
    • [DS92]
    • [DS92] A. Delshams and T.M. Seara. An asymptotic expression for the splitting of separatrices of the rapidly forced pendulum. Comm. Math. Phys., 150:433-463, 1992.
    • (1992) Comm. Math. Phys. , vol.150 , pp. 433-463
    • Delshams, A.1    Seara, T.M.2
  • 9
    • 0041485922 scopus 로고    scopus 로고
    • Splitting of separatrices in Hamiltonian systems with one and a half degrees of freedom
    • [DS97]
    • [DS97] A. Delshams and T.M. Seara. Splitting of separatrices in Hamiltonian systems with one and a half degrees of freedom. Math. Phys. Electron. J., 3(4):1-40, 1997.
    • (1997) Math. Phys. Electron. J. , vol.3 , Issue.4 , pp. 1-40
    • Delshams, A.1    Seara, T.M.2
  • 10
    • 0002445576 scopus 로고
    • Biasymptotic solutions of perturbed integrable Hamiltonian systems
    • [Eli94]
    • [Eli94] L.H. Eliasson. Biasymptotic solutions of perturbed integrable Hamiltonian systems. Bol. Soc. Brasil. Mat. (N.S.), 25(1):57-76, 1994.
    • (1994) Bol. Soc. Brasil. Mat. (N.S.) , vol.25 , Issue.1 , pp. 57-76
    • Eliasson, L.H.1
  • 11
    • 0000446018 scopus 로고
    • Twistless KAM tori, quasi flat homoclinic intersections, and other cancellations in the perturbation series of certain completely integrable Hamiltonian systems. a review
    • [Gal94]
    • [Gal94] G. Gallavotti. Twistless KAM tori, quasi flat homoclinic intersections, and other cancellations in the perturbation series of certain completely integrable Hamiltonian systems. A review. Rev. Math. Phys., 6(3):343-411, 1994.
    • (1994) Rev. Math. Phys. , vol.6 , Issue.3 , pp. 343-411
    • Gallavotti, G.1
  • 12
    • 0033241455 scopus 로고    scopus 로고
    • A proof of the exponentially small transversality of the separatrices for the standard map
    • [Gel99]
    • [Gel99] V.G. Gelfreich. A proof of the exponentially small transversality of the separatrices for the standard map. Comm. Math. Phys., 201(1):155-216, 1999.
    • (1999) Comm. Math. Phys. , vol.201 , Issue.1 , pp. 155-216
    • Gelfreich, V.G.1
  • 13
    • 13244292824 scopus 로고    scopus 로고
    • Splitting of separatrices for the Chirikov standard map
    • [Laz03]. The original Russian version appeared in 1984
    • [Laz03] V.F. Lazutkin. Splitting of separatrices for the Chirikov standard map. Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI), 300:25-55, 2003. The original Russian version appeared in 1984.
    • (2003) Zap. Nauchn. Sem. S.-Peterburg. Otdel. Mat. Inst. Steklov. (POMI) , vol.300 , pp. 25-55
    • Lazutkin, V.F.1
  • 14
    • 85088179441 scopus 로고    scopus 로고
    • On the splitting of invariant manifolds in multi-dimensional near-integrable Hamiltonian systems
    • [LMS03]
    • [LMS03] P. Lochak, J.-P. Marco, and D. Sauzin. On the splitting of invariant manifolds in multi-dimensional near-integrable Hamiltonian systems. Mem. Amer. Math. Soc., 163(775), 2003.
    • (2003) Mem. Amer. Math. Soc. , vol.163 , Issue.775
    • Lochak, P.1    Marco, J.-P.2    Sauzin, D.3
  • 15
    • 84980087693 scopus 로고
    • The analytic invariants of an area-preserving mapping near a hyperbolic fixed point
    • [Mos56]
    • [Mos56] J. Moser. The analytic invariants of an area-preserving mapping near a hyperbolic fixed point. Comm. Pure Appl. Math., 9:673-692, 1956.
    • (1956) Comm. Pure Appl. Math. , vol.9 , pp. 673-692
    • Moser, J.1
  • 16
    • 0034628167 scopus 로고    scopus 로고
    • Dynamics around simple resonant tori in nearly integrable Hamiltonian systems
    • [Nie00]
    • [Nie00] L. Niederman. Dynamics around simple resonant tori in nearly integrable Hamiltonian systems. J. Differential Equations, 161(1):1-41, 2000.
    • (2000) J. Differential Equations , vol.161 , Issue.1 , pp. 1-41
    • Niederman, L.1
  • 17
    • 77951516344 scopus 로고
    • Sur le problème des trois corps et les équations de la dynamique
    • [Poi90]
    • [Poi90] H. Poincaré. Sur le problème des trois corps et les équations de la dynamique. Acta Math., 13:1-270, 1890.
    • (1890) Acta Math. , vol.13 , pp. 1-270
    • Poincaré, H.1
  • 18
    • 0001193375 scopus 로고
    • Nekhoroshev estimates for quasi-convex Hamiltonian systems
    • [Pös93]
    • [Pös93] J. Pöschel. Nekhoroshev estimates for quasi-convex Hamiltonian systems. Math. Z., 213:187-216, 1993.
    • (1993) Math. Z. , vol.213 , pp. 187-216
    • Pöschel, J.1
  • 20
    • 5044222420 scopus 로고    scopus 로고
    • On the double pendulum: An example of double resonant situations
    • [PV04]
    • [PV04] A. Pumariño, and C. Valls. On the double pendulum: an example of double resonant situations. Discrete Contin. Dynam. Systems, 11(2/3):413-448, 2004.
    • (2004) Discrete Contin. Dynam. Systems , vol.11 , Issue.2-3 , pp. 413-448
    • Pumariño, A.1    Valls, C.2
  • 21
    • 0002682326 scopus 로고    scopus 로고
    • Existence of exponentially small separatrix splittings and homoclinic connections between whiskered tori in weakly hyperbolic near-integrable Hamiltonian systems
    • [RW98]
    • [RW98] M. Rudnev and S. Wiggins. Existence of exponentially small separatrix splittings and homoclinic connections between whiskered tori in weakly hyperbolic near-integrable Hamiltonian systems. Phys. D, 114:3-80, 1998.
    • (1998) Phys. D , vol.114 , pp. 3-80
    • Rudnev, M.1    Wiggins, S.2
  • 22
    • 0013269010 scopus 로고    scopus 로고
    • On a homoclinic splitting problem
    • [RW00]
    • [RW00] M. Rudnev and S. Wiggins. On a homoclinic splitting problem. Regul. Chaotic Dyn., 5(2):227-242, 2000.
    • (2000) Regul. Chaotic Dyn. , vol.5 , Issue.2 , pp. 227-242
    • Rudnev, M.1    Wiggins, S.2
  • 23
    • 0007322108 scopus 로고    scopus 로고
    • A new method for measuring the splitting of invariant manifolds
    • [Sau01]
    • [Sau01] D. Sauzin. A new method for measuring the splitting of invariant manifolds. Ann. Sci. École Norm. Sup. (4), 34(2):159-221, 2001.
    • (2001) Ann. Sci. École Norm. Sup. (4) , vol.34 , Issue.2 , pp. 159-221
    • Sauzin, D.1
  • 24
    • 0002761035 scopus 로고
    • Averaging under fast quasiperiodic forcing
    • [Sim94] J. Seimenis, editor. Held in Toruń, Poland, 28 June-2 July 1993. Plenum, New York
    • [Sim94] C. Simó. Averaging under fast quasiperiodic forcing. In J. Seimenis, editor, Hamiltonian Mechanics: Integrability and Chaotic Behavior, volume 331 of NATO ASI Ser. B: Phys., pages 13-34. Held in Toruń, Poland, 28 June-2 July 1993. Plenum, New York, 1994.
    • (1994) Hamiltonian Mechanics: Integrability and Chaotic Behavior, Volume 331 of NATO ASI Ser. B: Phys. , vol.331 , pp. 13-34
    • Simó, C.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.