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Volumn 22, Issue 4, 2009, Pages 783-810

Unique resonant normal forms for area-preserving maps at an elliptic fixed point

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EID: 67650735595     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/22/4/006     Document Type: Article
Times cited : (7)

References (20)
  • 1
  • 2
    • 0000878167 scopus 로고
    • Further reduction of the Takens-Bogdanov normal form
    • Baider A and Sanders J A 1992 Further reduction of the Takens-Bogdanov normal form J. Diff. Eqns 99 205-44
    • (1992) J. Diff. Eqns , vol.99 , Issue.2 , pp. 205-244
    • Baider, A.1    Sanders, J.A.2
  • 3
    • 67650718093 scopus 로고    scopus 로고
    • Generalized normal forms for two-dimensional systems of ordinary differential equations with linear and quadratic unperturbed parts
    • Basov V V and Fedotov A A 2007 Generalized normal forms for two-dimensional systems of ordinary differential equations with linear and quadratic unperturbed parts Vestn. St Petersburg Univ. Math. 40 6-26
    • (2007) Vestn. St Petersburg Univ. Math. , vol.40 , Issue.1 , pp. 6-26
    • Basov, V.V.1    Fedotov, A.A.2
  • 4
    • 43949170388 scopus 로고
    • Resonant normal forms, interpolating Hamiltonians and stability analysis of area preserving maps
    • Bazzani A, Giovannozzi M, Servizi G, Todesco E and Turchetti G 1993 Resonant normal forms, interpolating Hamiltonians and stability analysis of area preserving maps Physica D 64 66-97
    • (1993) Physica , vol.64 , Issue.1-3 , pp. 66-97
    • Bazzani, A.1    Giovannozzi, M.2    Servizi, G.3    Todesco, E.4    Turchetti, G.5
  • 5
    • 0002761467 scopus 로고
    • Formal normal form theorems for vector fields and some consequences for bifurcations in the volume preserving case
    • Broer H W 1981 Formal normal form theorems for vector fields and some consequences for bifurcations in the volume preserving case Dynamical Systems and Turbulence, Warwick, 1980 (Lecture Notes in Maths vol 898) ed D Rand and L-S Young (Berlin: Springer) pp 54-74
    • (1981) Dynamical Systems and Turbulence, Warwick, 1980 , vol.898 , pp. 54-74
    • Broer, H.W.1
  • 7
    • 44949236072 scopus 로고    scopus 로고
    • Generic Hopf-Neimark-Sacker bifurcations in feed forward systems
    • Broer H W and Vegter G 2008 Generic Hopf-Neimark-Sacker bifurcations in feed forward systems Nonlinearity 21 1547-78
    • (2008) Nonlinearity , vol.21 , Issue.7 , pp. 1547-1578
    • Broer, H.W.1    Vegter, G.2
  • 9
    • 84956092860 scopus 로고
    • The normal form of a Hamiltonian system
    • Bryuno A D 1988 The normal form of a Hamiltonian system Russ. Math. Surv. 43 25-66
    • (1988) Russ. Math. Surv. , vol.43 , Issue.1 , pp. 25-66
    • Bryuno, A.D.1
  • 10
    • 23044491410 scopus 로고    scopus 로고
    • Unique orbital normal form for vector fields of hopf-zero singularity
    • DOI 10.1007/s10884-005-2876-0
    • Chen G, Wang D and Yang J 2005 Unique orbital normal form for vector fields of Hopf-zero singularity J. Dynam. Diff. Eqns 17 3-20 (Pubitemid 41073354)
    • (2005) Journal of Dynamics and Differential Equations , vol.17 , Issue.1 , pp. 3-20
    • Chen, G.1    Wang, D.2    Yang, J.3
  • 11
    • 0000717287 scopus 로고
    • Canonical transformations depending on a small parameter
    • Deprit A 1969/1970 Canonical transformations depending on a small parameter Celest. Mech. 1 12-30
    • (1969) Celest. Mech. , vol.1 , Issue.1 , pp. 12-30
    • Deprit, A.1
  • 12
    • 84971996008 scopus 로고
    • The splitting of separatrices for analytic diffeomorphisms
    • Fontich E and Simó C 1990 The splitting of separatrices for analytic diffeomorphisms Ergodic Theory Dynam. Syst. 10 295-318
    • (1990) Ergodic Theory Dynam. Syst. , vol.10 , Issue.2 , pp. 295-318
    • Fontich, E.1    Simó, C.2
  • 13
    • 0035600465 scopus 로고    scopus 로고
    • Splitting of separatrices: Perturbation theory and exponential smallness
    • Gelfreich V and Lazutkin V 2001 Splitting of separatrices: perturbation theory and exponential smallness Russ. Math. Surv. 56 499-558
    • (2001) Russ. Math. Surv. , vol.56 , Issue.3 , pp. 499-558
    • Gelfreich, V.1    Lazutkin, V.2
  • 14
    • 0001454797 scopus 로고
    • Generic bifurcation of Hamiltonian systems with symmetry
    • Golubitsky M and Stewart I 1987 Generic bifurcation of Hamiltonian systems with symmetry Physica D 24 391-405 (with an appendix by Jerrold Marsden)
    • (1987) Physica , vol.24 , Issue.1-3 , pp. 391-405
    • Golubitsky, M.1    Stewart, I.2
  • 15
    • 0000107874 scopus 로고    scopus 로고
    • Linear grading function and further reduction of normal forms
    • Kokubu H, Oka H and Wang D 1996 Linear grading function and further reduction of normal forms J. Diff. Eqns 132 293-318
    • (1996) J. Diff. Eqns , vol.132 , Issue.2 , pp. 293-318
    • Kokubu, H.1    Oka, H.2    Wang, D.3
  • 16
    • 24944545967 scopus 로고    scopus 로고
    • Elements of applied bifurcation theory
    • pp
    • Kuznetsov Y A 2004 Elements of applied bifurcation theory Applied Mathematical Sciences vol 112 3rd edn (New York: Springer) 631 pp
    • (2004) Applied Mathematical Sciences , vol.112 , pp. 631
    • Kuznetsov, Y.A.1
  • 17
    • 84980087693 scopus 로고
    • The analytic invariants of an area-preserving mapping near a hyperbolic fixed point
    • Moser J 1956 The analytic invariants of an area-preserving mapping near a hyperbolic fixed point Commun. Pure Appl. Math. 9 673-92
    • (1956) Commun. Pure Appl. Math. , vol.9 , Issue.4 , pp. 673-692
    • Moser, J.1
  • 18
    • 84980078160 scopus 로고
    • Vereinfachter Beweis eines Satzes von J. Moser
    • Siegel C L 1957 Vereinfachter Beweis eines Satzes von J. Moser Commun. Pure Appl. Math. 10 305-9 (in German)
    • (1957) Commun. Pure Appl. Math. , vol.10 , Issue.3 , pp. 305-309
    • Siegel, C.L.1
  • 19
    • 0002533366 scopus 로고
    • Forced oscillations and bifurcations, Applications of Global Analysis, i (Utrecht, 1973)
    • Takens F 1974 Forced oscillations and bifurcations, Applications of Global Analysis, I (Utrecht, 1973) Commun. Math. Inst. Univ. Utrecht 3 1-59
    • (1974) Commun. Math. Inst. Univ. Utrecht , vol.3 , pp. 1-59
    • Takens, F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.