메뉴 건너뛰기




Volumn 21, Issue 1-4, 1999, Pages 287-310

Computation of normal forms of Hamiltonian systems in the presence of Poisson commuting integrals

Author keywords

Computer algebra; First integrals; Hamiltonian vector fields; Joint normal form

Indexed keywords


EID: 0033469479     PISSN: 10171398     EISSN: None     Source Type: Journal    
DOI: 10.1023/a:1019177917586     Document Type: Article
Times cited : (3)

References (43)
  • 2
    • 0032486021 scopus 로고    scopus 로고
    • Research of periodic solutions of the nonintegrable Hénon-Heiles system by the Lindstedt-Poincaré method
    • S. Benbachir, Research of periodic solutions of the nonintegrable Hénon-Heiles system by the Lindstedt-Poincaré method, J. Phys. A 31 (1998) 5083-5103.
    • (1998) J. Phys. A , vol.31 , pp. 5083-5103
    • Benbachir, S.1
  • 3
    • 0042675835 scopus 로고
    • Colloq. Publ. 9 Amer. Math. Soc., Providence, RI
    • G.D. Birkhoff, Dynamical Systems, 2nd ed., Colloq. Publ. 9 (Amer. Math. Soc., Providence, RI, 1927) 54.
    • (1927) Dynamical Systems, 2nd Ed. , pp. 54
    • Birkhoff, G.D.1
  • 4
    • 0001055171 scopus 로고
    • Analytical form of differential equations II
    • A.D. Bruno (Brjuno), Analytical form of differential equations II, Trans. Moscow Math. Soc. 26 (1972) 199-239.
    • (1972) Trans. Moscow Math. Soc. , vol.26 , pp. 199-239
    • Bruno, A.D.1
  • 7
    • 0000210320 scopus 로고
    • Symmetries and convergence of normalizing transformations
    • A.D. Bruno and S. Walcher, Symmetries and convergence of normalizing transformations, J. Math. Anal. Appl. 183 (1994) 571-576.
    • (1994) J. Math. Anal. Appl. , vol.183 , pp. 571-576
    • Bruno, A.D.1    Walcher, S.2
  • 8
    • 34249917727 scopus 로고
    • On the stability of the Lagrangian points in the spacial restricted three body problem
    • A. Celletti and A. Giorgilli, On the stability of the Lagrangian points in the spacial restricted three body problem, Celest. Mech. 50 (1991) 31-58.
    • (1991) Celest. Mech. , vol.50 , pp. 31-58
    • Celletti, A.1    Giorgilli, A.2
  • 12
    • 0030122291 scopus 로고    scopus 로고
    • On the convergence of normalizing transformations in the presence of symmetries
    • G. Cicogna, On the convergence of normalizing transformations in the presence of symmetries, J. Math. Anal. Appl. 199 (1996) 243.
    • (1996) J. Math. Anal. Appl. , vol.199 , pp. 243
    • Cicogna, G.1
  • 13
    • 21344484282 scopus 로고
    • Poincaré normal forms and Lie point symmetries
    • G. Cicogna and G. Gaeta, Poincaré normal forms and Lie point symmetries, J. Phys. A 27 (1994) 461-476.
    • (1994) J. Phys. A , vol.27 , pp. 461-476
    • Cicogna, G.1    Gaeta, G.2
  • 14
    • 21844526765 scopus 로고
    • Normal forms and nonlinear symmetries
    • G. Cicogna and G. Gaeta, Normal forms and nonlinear symmetries, J. Phys. A 27 (1994) 7115-7124.
    • (1994) J. Phys. A , vol.27 , pp. 7115-7124
    • Cicogna, G.1    Gaeta, G.2
  • 16
    • 0043176892 scopus 로고    scopus 로고
    • Normal form method for symbolic creation of approximate solutions of nonlinear mechanical systems
    • Marseille May 3-7
    • J. Della Dora, J. Mikram and F. Zinoun, Normal form method for symbolic creation of approximate solutions of nonlinear mechanical systems, CATHODE 2, CIRM Luminy, Marseille (May 3-7, 1999) (http://www-lmc.imag.fr/CATHODE2/Cirm/abstract/).
    • (1999) CATHODE 2, CIRM Luminy
    • Della Dora, J.1    Mikram, J.2    Zinoun, F.3
  • 18
    • 0000717287 scopus 로고
    • Canonical transformation depending on a small parameter
    • A. Deprit, Canonical transformation depending on a small parameter, Celest. Mech. 1 (1969) 12-30.
    • (1969) Celest. Mech. , vol.1 , pp. 12-30
    • Deprit, A.1
  • 19
    • 0032028740 scopus 로고    scopus 로고
    • A symbolic approximation of periodic solutions of the Hénon-Heiles system by the normal form method
    • V.F. Edneral, A symbolic approximation of periodic solutions of the Hénon-Heiles system by the normal form method, Math. Comput. Simulation 45 (1998) 445-463.
    • (1998) Math. Comput. Simulation , vol.45 , pp. 445-463
    • Edneral, V.F.1
  • 20
    • 0001963733 scopus 로고
    • Monodromy and the Kowalevskaya top
    • J.-P. Françoise, Monodromy and the Kowalevskaya top, Astérisque 150/151 (1987) 87-108.
    • (1987) Astérisque , vol.150-151 , pp. 87-108
    • Françoise, J.-P.1
  • 21
    • 0000980927 scopus 로고
    • Bifurcations of invariant manifolds in the generalized Hénon-Heiles system
    • L. Gavrilov, Bifurcations of invariant manifolds in the generalized Hénon-Heiles system, Phys. D 34 (1989) 223-239.
    • (1989) Phys. D , vol.34 , pp. 223-239
    • Gavrilov, L.1
  • 23
    • 0018446732 scopus 로고
    • A computer program for integrals of motion
    • A. Giorgilly, A computer program for integrals of motion, Comput. Phys. Commun. 16 (1979) 331-343.
    • (1979) Comput. Phys. Commun. , vol.16 , pp. 331-343
    • Giorgilly, A.1
  • 24
    • 0000330285 scopus 로고
    • Formal integrals for an autonomous Hamiltonian system near an equilibrium point
    • A. Giorgilli and L. Galgani, Formal integrals for an autonomous Hamiltonian system near an equilibrium point, Celest. Mech. 17 (1978) 267-280.
    • (1978) Celest. Mech. , vol.17 , pp. 267-280
    • Giorgilli, A.1    Galgani, L.2
  • 26
    • 0002519122 scopus 로고
    • The applicability of the third integral of motion: Some numerical experiments
    • M. Hénon and C. Heiles, The applicability of the third integral of motion: Some numerical experiments, Astronom. J. 69 (1964) 73-79.
    • (1964) Astronom. J. , vol.69 , pp. 73-79
    • Hénon, M.1    Heiles, C.2
  • 27
    • 0000628533 scopus 로고
    • Theory of general perturbations with unspecified canonical variables
    • G.I. Hori, Theory of general perturbations with unspecified canonical variables, J. Japan Astron. Soc. 18 (1966) 287-296.
    • (1966) J. Japan Astron. Soc. , vol.18 , pp. 287-296
    • Hori, G.I.1
  • 28
    • 51249174723 scopus 로고
    • Convergence of Birkhoff normal forms for integrable systems
    • H. Ito, Convergence of Birkhoff normal forms for integrable systems, Comment. Math. Helv. 64 (1989) 412-461.
    • (1989) Comment. Math. Helv. , vol.64 , pp. 412-461
    • Ito, H.1
  • 29
    • 0004278751 scopus 로고
    • Some aspects of integrability and action-angle variables
    • H. Ito, Some aspects of integrability and action-angle variables, Sugaku Expositions 3(2) (1990) 213-232.
    • (1990) Sugaku Expositions , vol.3 , Issue.2 , pp. 213-232
    • Ito, H.1
  • 30
    • 0001110443 scopus 로고
    • Integrability of Hamiltonian systems and Birkhoff normal forms in the simple resonance case
    • H. Ito, Integrability of Hamiltonian systems and Birkhoff normal forms in the simple resonance case, Math. Ann. 292 (1992) 411-444.
    • (1992) Math. Ann. , vol.292 , pp. 411-444
    • Ito, H.1
  • 32
    • 0000970971 scopus 로고
    • Note sur l'intégration des équations différentielles de la dynamique
    • J. Liouville, Note sur l'intégration des équations différentielles de la dynamique, J. Math. Pures Appl. 20 (1855) 137-138.
    • (1855) J. Math. Pures Appl. , vol.20 , pp. 137-138
    • Liouville, J.1
  • 33
    • 0003083471 scopus 로고
    • A new algorithm for Lie transformation
    • W.A. Mersman, A new algorithm for Lie transformation, Celest. Mech. 3 (1970) 81-89.
    • (1970) Celest. Mech. , vol.3 , pp. 81-89
    • Mersman, W.A.1
  • 34
    • 0042675833 scopus 로고    scopus 로고
    • On structure preserving normal forms of Hamiltonian dynamical systems
    • Prague August 9-11
    • J. Mikram and F. Zinoun, On structure preserving normal forms of Hamiltonian dynamical systems, in: 4th Internat. Conf. on Application of Computer Algebra, IMACS-ACA, Prague (August 9-11, 1998) (http://math.unm.edu/ACA/1998/sessions/dynamical/).
    • (1998) 4th Internat. Conf. on Application of Computer Algebra, IMACS-ACA
    • Mikram, J.1    Zinoun, F.2
  • 37
    • 0010338472 scopus 로고
    • Normal forms and center manifold calculation on MACSYMA
    • ed. R. Pavelle
    • R.H. Rand and W.L. Keith, Normal forms and center manifold calculation on MACSYMA, in: Applications of Computer Algebra, ed. R. Pavelle (1987).
    • (1987) Applications of Computer Algebra
    • Rand, R.H.1    Keith, W.L.2
  • 38
    • 0006998795 scopus 로고
    • On the existence of normal modes vibrations of nonlinear systems with two degrees of freedom
    • R.M. Rosenberg, On the existence of normal modes vibrations of nonlinear systems with two degrees of freedom, Quart. Appl. Math. 22 (1964) 217-234.
    • (1964) Quart. Appl. Math. , vol.22 , pp. 217-234
    • Rosenberg, R.M.1
  • 39
    • 0000757375 scopus 로고
    • Über das Verhalten analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung
    • H. Rüssmann, Über das Verhalten analytischer Hamiltonscher Differentialgleichungen in der Nähe einer Gleichgewichtslösung, Math. Ann. 154 (1964) 285-300.
    • (1964) Math. Ann. , vol.154 , pp. 285-300
    • Rüssmann, H.1
  • 40
    • 84874778356 scopus 로고
    • An algorithm for the computation of normal forms and invariant manifolds
    • ed. M. Bronstein, Kiev, Ukraine (July 1993) ACM, New York
    • L. Vallier, An algorithm for the computation of normal forms and invariant manifolds, in: Proc. of the 1993 Internat. Symp. on Symbolic and Algebraic Computation, ed. M. Bronstein, Kiev, Ukraine (July 1993) (ACM, New York, 1993) pp. 225-234.
    • (1993) Proc. of the 1993 Internat. Symp. on Symbolic and Algebraic Computation , pp. 225-234
    • Vallier, L.1
  • 41
    • 0000132941 scopus 로고
    • Sur certains systèmes dynamiques séparables
    • J. Vey, Sur certains systèmes dynamiques séparables, Amer. J. Math. 100 (1978) 591-614.
    • (1978) Amer. J. Math. , vol.100 , pp. 591-614
    • Vey, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.