메뉴 건너뛰기




Volumn 135, Issue 9, 2007, Pages 2887-2891

From an iteration formula to Poincaré's isochronous center theorem for holomorphic vector fields

Author keywords

Holomorphic differential equation; Ordinary differential equation

Indexed keywords


EID: 70449468492     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-07-08802-8     Document Type: Article
Times cited : (4)

References (19)
  • 1
    • 0003595232 scopus 로고
    • second edition, Translated by Joseph Szücs, English Translated Edited by Mark Levi, Springer-Verlag, MR0947141 89h:58049
    • Arnold, V. I. Geometrical methods in the theory of ordinary differential equations, second edition, Translated by Joseph Szücs, English Translated Edited by Mark Levi, Springer-Verlag, 1988. MR0947141 (89h:58049)
    • (1988) Geometrical Methods in the Theory of Ordinary Differential Equations
    • Arnold, V.I.1
  • 3
    • 0013171019 scopus 로고
    • Conformal equivalence of analytic flows
    • MR0447674 56:5984
    • Brickman, L. & Thomas, E. S., Conformal equivalence of analytic flows, J. Differential Equations 25 (1977), no. 3, 310-324. MR0447674 (56:5984)
    • (1977) J. Differential Equations , vol.25 , Issue.3 , pp. 310-324
    • Brickman, L.1    Thomas, E.S.2
  • 5
    • 63949086501 scopus 로고    scopus 로고
    • The centre conditions for a certain cubic system, Planar nonlinear dynamical systems
    • Delft, 1995, MR1660202 99i:34041
    • Cherkas, L. A., Romanovskii, V. G. & Zoladek, H., The centre conditions for a certain cubic system, Planar nonlinear dynamical systems (Delft, 1995), Differential Equations Dynam. Systems 5 (1997), no. 3-4, 299-302. MR1660202 (99i:34041)
    • (1997) Differential Equations Dynam. Systems , vol.5 , Issue.3-4 , pp. 299-302
    • Cherkas, L.A.1    Romanovskii, V.G.2    Zoladek, H.3
  • 6
    • 0039971668 scopus 로고    scopus 로고
    • Isochronous centers in planar polynomial systems
    • MR1427732 97k:34058
    • Christopher, C. J. & Devlin, J., Isochronous centers in planar polynomial systems, SIAM J. Math. Anal. 28 (1997), no. 1, 162-177. MR1427732 (97k:34058)
    • (1997) SIAM J. Math. Anal. , vol.28 , Issue.1 , pp. 162-177
    • Christopher, C.J.1    Devlin, J.2
  • 7
    • 70449468493 scopus 로고
    • The center of oscillation versus the textbook writers of the early 18th century. From ancient omens to statistical mechanics
    • Univ. Lib. Copenhagen, Copenhagen, MR0961883 90m:01015
    • Feigenbaum, L., The center of oscillation versus the textbook writers of the early 18th century. From ancient omens to statistical mechanics, 193-202, Acta Hist. Sci. Nat. Med., 39, Univ. Lib. Copenhagen, Copenhagen, 1987. MR0961883 (90m:01015)
    • (1987) Acta Hist. Sci. Nat. Med. , vol.39 , pp. 193-202
    • Feigenbaum, L.1
  • 8
    • 30444440589 scopus 로고    scopus 로고
    • Isochronous systems and perturbation theory
    • MR2117189 2005h:34074
    • Francoise, J.-P., Isochronous systems and perturbation theory, Journal Nonlinear Math. Phys., Vol. 12, Supplement 1 (2005), 315-326. MR2117189 (2005h:34074)
    • (2005) Journal Nonlinear Math. Phys. , vol.12 , Issue.1 SUPPL. , pp. 315-326
    • Francoise, J.-P.1
  • 9
    • 30444453458 scopus 로고
    • Dynamical systems with regular hand-side
    • Gregor, J., Dynamical systems with regular hand-side, Pokroky Mat. Fys. Astronom. 3 (1958), 153-160.
    • (1958) Pokroky Mat. Fys. Astronom , vol.3 , pp. 153-160
    • Gregor, J.1
  • 10
    • 8744241884 scopus 로고
    • Notes on meromorphic dynamical systems, I-III
    • MR0194661 33:2870a
    • Hajek, O., Notes on meromorphic dynamical systems, I-III, Czechoslovak Math. J. 16 (1966), 14-40. MR0194661 (33:2870a);
    • (1966) Czechoslovak Math. J. , vol.16 , pp. 14-40
    • Hajek, O.1
  • 11
    • 77950679738 scopus 로고    scopus 로고
    • MR0194662 33:2870b
    • MR0194662 (33:2870b);
  • 12
    • 77950665433 scopus 로고    scopus 로고
    • MR0194663 33:2870c
    • MR0194663 (33:2870c)
  • 13
    • 0346458476 scopus 로고
    • Isochronicity of center for certain systems of differential equations
    • MR0197863 33:6023
    • Lukashevich, N. A., Isochronicity of center for certain systems of differential equations, Differ. Uravn. 1 (1965), 295-302. MR0197863 (33:6023)
    • (1965) Differ. Uravn , vol.1 , pp. 295-302
    • Lukashevich, N.A.1
  • 14
    • 0011827356 scopus 로고    scopus 로고
    • Dynamics in one complex variable: Introductory lectures
    • MR1721240 2002i:37057
    • Milnor, J., Dynamics in One Complex Variable: Introductory Lectures, Friedrick Vieweg & Son, 2000. MR1721240 (2002i:37057)
    • (2000) Friedrick Vieweg & Son
    • Milnor, J.1
  • 15
    • 33746706911 scopus 로고    scopus 로고
    • Centre families in two-dimensional complex holomorphic dynamical systems
    • MR1639872 99d:34010
    • Needham, D. J. & McAllister, S., Centre families in two-dimensional complex holomorphic dynamical systems, R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. 454 (1998), no. 1976, 2267-2278. MR1639872 (99d:34010)
    • (1998) R. Soc. Lond. Proc. Ser. A Math. Phys. Eng. Sci. , vol.454 , Issue.1976 , pp. 2267-2278
    • Needham, D.J.1    McAllister, S.2
  • 16
    • 0038858635 scopus 로고
    • On periodic solutions of polynomial ODEs in the plane
    • MR0747404 86g:34054
    • Paluszny, M., On periodic solutions of polynomial ODEs in the plane, J. Differential Equations 53 (1984), no. 1, 24-29. MR0747404 (86g:34054)
    • (1984) J. Differential Equations , vol.53 , Issue.1 , pp. 24-29
    • Paluszny, M.1
  • 17
    • 0042710621 scopus 로고    scopus 로고
    • Dynamics of commuting systems on two-dimensional manifolds
    • MR1625543 99f:34071
    • Sabatini, M., Dynamics of commuting systems on two-dimensional manifolds, Ann. Mat. Pura Appl. (4) 173 (1997), 213-232. MR1625543 (99f:34071)
    • (1997) Ann. Mat. Pura Appl. , vol.173 , Issue.4 , pp. 213-232
    • Sabatini, M.1
  • 18
    • 0000353375 scopus 로고
    • Regularity properties of the period function near a center of a planar vector field
    • MR1186791 93j:34061
    • Villarini, M., Regularity properties of the period function near a center of a planar vector field, Nonlinear Anal. 19 (1992), no. 8, 787-803. MR1186791 (93j:34061)
    • (1992) Nonlinear Anal. , vol.19 , Issue.8 , pp. 787-803
    • Villarini, M.1
  • 19
    • 77950675795 scopus 로고    scopus 로고
    • Fixed point indices and invariant periodic sets of holomorphic systems
    • to appear in
    • Zhang, G. Y., Fixed Point Indices and Invariant Periodic Sets of Holomorphic Systems, to appear in Proc. Amer. Math. Soc.
    • Proc. Amer. Math. Soc.
    • Zhang, G.Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.