메뉴 건너뛰기




Volumn 25, Issue 2, 2013, Pages 335-392

Exponentially Small Heteroclinic Breakdown in the Generic Hopf-Zero Singularity

Author keywords

Exponentially small phenomena; Hopf zero singularity; Singular perturbation theory; Splitting of separatrices

Indexed keywords


EID: 84877838481     PISSN: 10407294     EISSN: 15729222     Source Type: Journal    
DOI: 10.1007/s10884-013-9297-2     Document Type: Article
Times cited : (22)

References (20)
  • 2
    • 84867945302 scopus 로고    scopus 로고
    • Breakdown of heteroclinic orbits for some analytic unfoldings of the Hopf-zero singularity
    • doi:10.1007/s00332-005-0736-z
    • Baldomá, I., Seara, T. M.: Breakdown of heteroclinic orbits for some analytic unfoldings of the Hopf-zero singularity. J. Nonlinear Sci. 16(6), 543-582 (2006). doi: 10. 1007/s00332-005-0736-z.
    • (2006) J. Nonlinear Sci. , vol.16 , Issue.6 , pp. 543-582
    • Baldomá, I.1    Seara, T.M.2
  • 3
    • 73149112791 scopus 로고    scopus 로고
    • The inner equation for generic analytic unfoldings of the Hopf-zero singularity
    • Baldomá, I., Seara, T. M.: The inner equation for generic analytic unfoldings of the Hopf-zero singularity. Discret. Contin. Dyn. Syst. Ser. B 10(2-3), 323-347 (2008).
    • (2008) Discret. Contin. Dyn. Syst. Ser. B , vol.10 , Issue.2-3 , pp. 323-347
    • Baldomá, I.1    Seara, T.M.2
  • 4
    • 0001231858 scopus 로고
    • Subordinate Šil'nikov bifurcations near some singularities of vector fields having low codimension
    • doi:10.1017/S0143385700002613
    • Broer, H., Vegter, G.: Subordinate Šil'nikov bifurcations near some singularities of vector fields having low codimension. Ergod. Theory Dyn. Syst. 4, 509-525 (1984). doi: 10. 1017/S0143385700002613.
    • (1984) Ergod. Theory Dyn. Syst. , vol.4 , pp. 509-525
    • Broer, H.1    Vegter, G.2
  • 5
    • 0041485922 scopus 로고    scopus 로고
    • Splitting of separatrices in Hamiltonian systems with one and a half degrees of freedom
    • Delshams, A., Seara, T. M.: Splitting of separatrices in Hamiltonian systems with one and a half degrees of freedom. Math. Phys. Electron. J. 3(4), 40 (1997).
    • (1997) Math. Phys. Electron. J , vol.3 , Issue.4 , pp. 40
    • Delshams, A.1    Seara, T.M.2
  • 6
    • 81155151729 scopus 로고    scopus 로고
    • About the unfolding of a Hopf-zero singularity
    • (preprint)
    • Dumortier, F., Ibánez, S., Kokubu, H., Simó, C.: About the unfolding of a Hopf-zero singularity (2012) (preprint).
    • (2012)
    • Dumortier, F.1    Ibánez, S.2    Kokubu, H.3    Simó, C.4
  • 7
    • 0000664107 scopus 로고    scopus 로고
    • Melnikov method and exponentially small splitting of separatrices
    • doi: 10. 1016/S0167-2789(96)00133-9
    • Gelfreich, V. G.: Melnikov method and exponentially small splitting of separatrices. Phys. D 101(3-4), 227-248 (1997). doi: 10. 1016/S0167-2789(96)00133-9.
    • (1997) Phys. D , vol.101 , Issue.3-4 , pp. 227-248
    • Gelfreich, V.G.1
  • 8
    • 78149443808 scopus 로고    scopus 로고
    • Exponentially small splitting for the pendulum: a classical problem revisited
    • doi: s10. 1007/s00332-010-9068-8
    • Guardia, M., Olivé, C., Seara, T. M.: Exponentially small splitting for the pendulum: a classical problem revisited. J. Nonlinear Sci. 20(5), 595-685 (2010). doi: 10. 1007/s00332-010-9068-8.
    • (2010) J. Nonlinear Sci , vol.20 , Issue.5
    • Guardia, M.1    Olivé, C.2    Seara, T.M.3
  • 12
    • 0001834849 scopus 로고
    • On the stability of a center for time-periodic perturbations
    • Mel'nikov, V. K.: On the stability of a center for time-periodic perturbations. Trudy Moskov. Mat. Obšč. 12, 3-52 (1963).
    • (1963) Trudy Moskov. Mat. Obšč. , vol.12 , pp. 3-52
    • Mel'nikov, V.K.1
  • 13
    • 0007322108 scopus 로고    scopus 로고
    • A new method for measuring the splitting of invariant manifolds
    • doi: 10. 1016/S0012-9593(00), 01063-6
    • Sauzin, D.: A new method for measuring the splitting of invariant manifolds. Ann. Sci. École Norm. Sup. (4) 34(2), 159-221 (2001). doi: 10. 1016/S0012-9593(00), 01063-6.
    • (2001) Ann. Sci. École Norm. Sup. (4) , vol.34 , Issue.2 , pp. 159-221
    • Sauzin, D.1
  • 14
    • 0001546143 scopus 로고
    • A case of the existence of a denumerable set of periodic motions
    • Šil'nikov, L. P.: A case of the existence of a denumerable set of periodic motions. Dokl. Akad. Nauk SSSR 160, 558-561 (1965).
    • (1965) Dokl. Akad. Nauk SSSR , vol.160 , pp. 558-561
    • Šil'nikov, L.P.1
  • 15
    • 0002997858 scopus 로고
    • The existence of a denumerable set of periodic motions in four-dimensional space in an extended neighborhood of a saddle-focus
    • Šil'nikov, L. P.: The existence of a denumerable set of periodic motions in four-dimensional space in an extended neighborhood of a saddle-focus. Sov. Math. Dokl. 8, 54-58 (1967).
    • (1967) Sov. Math. Dokl. , vol.8 , pp. 54-58
    • Šil'nikov, L.P.1
  • 16
    • 0000731315 scopus 로고
    • On the discontinuity of arbitrary constants which appear in divergent developments
    • Stokes, G. G.: On the discontinuity of arbitrary constants which appear in divergent developments. Trans. Camb. Phil. Soc. 10, 106-128 (1864).
    • (1864) Trans. Camb. Phil. Soc. , vol.10 , pp. 106-128
    • Stokes, G.G.1
  • 17
    • 34250593478 scopus 로고
    • On the discontinuity of arbitrary constants that appear as multipliers of semi-convergent series
    • doi: 10. 1007/BF02415503
    • Stokes, G. G.: On the discontinuity of arbitrary constants that appear as multipliers of semi-convergent series. Acta Math. 26(1), 393-397 (1902). doi: 10. 1007/BF02415503.
    • (1902) Acta Math , vol.26 , Issue.1 , pp. 393-397
    • Stokes, G.G.1
  • 20
    • 0031312703 scopus 로고    scopus 로고
    • Splitting of separatrices for a pendulum with rapidly oscillating suspension point
    • Treschev, D. V.: Splitting of separatrices for a pendulum with rapidly oscillating suspension point. Russ. J. Math. Phys. 5(1), 63-98 (1997).
    • (1997) Russ. J. Math. Phys , vol.5 , Issue.1 , pp. 63-98
    • Treschev, D.V.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.