메뉴 건너뛰기




Volumn 166, Issue 2, 2004, Pages 465-476

Implementation of a new algorithm of computation of the Poincaré-Liapunov constants

Author keywords

Computer algebra system; Gr bner basis; Poincar Liapunov constants; Small amplitude limit cycles; The center problem

Indexed keywords

ALGORITHMS; BOOLEAN ALGEBRA; FUNCTIONS; LYAPUNOV METHODS; PERTURBATION TECHNIQUES; PROBLEM SOLVING;

EID: 1542634930     PISSN: 03770427     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.cam.2003.08.043     Document Type: Article
Times cited : (30)

References (31)
  • 1
    • 0012780334 scopus 로고    scopus 로고
    • Computing the Poincaré-Liapunov constants
    • Alwash M.A.M. Computing the Poincaré-Liapunov constants Differential Equations Dyn. Systems 6 3 1998 349-361
    • (1998) Differential Equations Dyn. Systems , vol.6 , Issue.3 , pp. 349-361
    • Alwash, M.A.M.1
  • 2
    • 0000495631 scopus 로고
    • On the number of limit cycles which appear with the variation of coefficients from an equilibrium position of focus or center type
    • Bautin N.N. On the number of limit cycles which appear with the variation of coefficients from an equilibrium position of focus or center type Mat. Sb. 30 72 1952 181-196
    • (1952) Mat. Sb. , vol.30 , Issue.72 , pp. 181-196
    • Bautin, N.N.1
  • 4
    • 84976168837 scopus 로고
    • The number of limit cycles of certain polynomial differential equations
    • Blows T.R. Lloyd N.G. The number of limit cycles of certain polynomial differential equations Proc. Roy. Soc. Edinburgh 98 A 1984 215-239
    • (1984) Proc. Roy. Soc. Edinburgh , vol.98 , Issue.A , pp. 215-239
    • Blows, T.R.1    Lloyd, N.G.2
  • 5
    • 0003089046 scopus 로고    scopus 로고
    • Integrability of a linear center perturbed by fourth degree homogeneous polynomial
    • Chavarriga J. Giné J. Integrability of a linear center perturbed by fourth degree homogeneous polynomial Publ. Mat. 40 1 1996 21-39
    • (1996) Publ. Mat. , vol.40 , Issue.1 , pp. 21-39
    • Chavarriga, J.1    Giné, J.2
  • 6
    • 0001302034 scopus 로고    scopus 로고
    • Integrability of a linear center perturbed by a fifth degree homogeneous polynomial
    • Chavarriga J. Giné J. Integrability of a linear center perturbed by a fifth degree homogeneous polynomial Publ. Mat. 41 2 1997 335-356
    • (1997) Publ. Mat. , vol.41 , Issue.2 , pp. 335-356
    • Chavarriga, J.1    Giné, J.2
  • 7
    • 0013185298 scopus 로고
    • Sur la théorie des centres
    • Chazy J. Sur la théorie des centres C. R. Acad. Sci. Paris 221 1947 7-10
    • (1947) C. R. Acad. Sci. Paris , vol.221 , pp. 7-10
    • Chazy, J.1
  • 8
    • 0001287885 scopus 로고
    • Relative position and number of limit cycles of a quadratic differential system
    • Lansun Chen Mingshu Wang Relative position and number of limit cycles of a quadratic differential system Acta Math. Sinica 22 1979 751-758
    • (1979) Acta Math. Sinica , vol.22 , pp. 751-758
    • Chen, L.1    Wang, M.2
  • 12
    • 0030546995 scopus 로고    scopus 로고
    • Successive derivatives of a first return map
    • Françoise J.P. Successive derivatives of a first return map Ergodic Theory Dyn. Systems 16 1 1996 87-96
    • (1996) Ergodic Theory Dyn. Systems , vol.16 , Issue.1 , pp. 87-96
    • Françoise, J.P.1
  • 13
    • 0000311624 scopus 로고
    • Computer algebra methods and the stability of differential systems
    • Françoise J.P. Pons R. Computer algebra methods and the stability of differential systems Random Comput. Dyn. 3 4 1995 265-287
    • (1995) Random Comput. Dyn. , vol.3 , Issue.4 , pp. 265-287
    • Françoise, J.P.1    Pons, R.2
  • 14
    • 0040532239 scopus 로고    scopus 로고
    • An analytic-numerical method of computation of the Liapunov and period constants derived from their algebraic structure
    • Gasull A. Guillamon A. Manosa V. An analytic-numerical method of computation of the Liapunov and period constants derived from their algebraic structure SIAM J. Numer. Anal. 36 4 1999 1030-1043
    • (1999) SIAM J. Numer. Anal. , vol.36 , Issue.4 , pp. 1030-1043
    • Gasull, A.1    Guillamon, A.2    Manosa, V.3
  • 15
    • 0000763063 scopus 로고    scopus 로고
    • On the nonexistence, existence, and uniqueness of limit cycles
    • Giacomini H. Llibre J. Viano M. On the nonexistence, existence, and uniqueness of limit cycles Nonlinearity 9 1999 501-516
    • (1999) Nonlinearity , vol.9 , pp. 501-516
    • Giacomini, H.1    Llibre, J.2    Viano, M.3
  • 16
    • 0036567134 scopus 로고    scopus 로고
    • Conditions for the existence of a center for the Kukles homogeneous systems
    • Giné J. Conditions for the existence of a center for the Kukles homogeneous systems Comput. Math. Appl. 43 2002 1261-1269
    • (2002) Comput. Math. Appl. , vol.43 , pp. 1261-1269
    • Giné, J.1
  • 17
    • 0010569308 scopus 로고    scopus 로고
    • On the Poincaré-Liapunov constants and the Poincaré series
    • Warsaw
    • Giné J. Santallusia X. On the Poincaré-Liapunov constants and the Poincaré series Appl. Math. (Warsaw) 28 1 2001 17-30
    • (2001) Appl. Math. , vol.28 , Issue.1 , pp. 17-30
    • Giné, J.1    Santallusia, X.2
  • 18
    • 0012778404 scopus 로고
    • Finiteness theorems for limit cycles
    • Ilyashenko Yu.S. Finiteness theorems for limit cycles Russian Math. Surveys 40 1990 143-200
    • (1990) Russian Math. Surveys , vol.40 , pp. 143-200
    • Ilyashenko, Yu.S.1
  • 19
    • 0003304975 scopus 로고
    • Problème général de la stabilité du mouvement
    • Princeton University Press, Princeton, NJ
    • M.A. Liapunov, Problème général de la stabilité du mouvement, Annal of Mathematics Studies, Vol. 17, Princeton University Press, Princeton, NJ, 1947.
    • (1947) Annal of Mathematics Studies , vol.17
    • Liapunov, M.A.1
  • 20
    • 0001413231 scopus 로고
    • REDUCE and the bifurcation of limit cycles
    • Lloyd N.G. Pearson J.M. REDUCE and the bifurcation of limit cycles J. Symbolic Comput. 9 1990 215-224
    • (1990) J. Symbolic Comput. , vol.9 , pp. 215-224
    • Lloyd, N.G.1    Pearson, J.M.2
  • 22
    • 0000663138 scopus 로고
    • Mémoire sur les courbes définies par les équations différentielles
    • Poincaré H. Mémoire sur les courbes définies par les équations différentielles J. de Mathématiques 37 1881-1882 375-422
    • (1881) J. de Mathématiques , vol.37 , pp. 375-422
    • Poincaré, H.1
  • 23
    • 0007220843 scopus 로고
    • Mémoire sur les courbes définies par les équations différentielles
    • Poincaré H. Mémoire sur les courbes définies par les équations différentielles J. de Mathématiques 8 1881-1882 251-296
    • (1881) J. de Mathématiques , vol.8 , pp. 251-296
    • Poincaré, H.1
  • 26
    • 0003244212 scopus 로고    scopus 로고
    • Bifurcation of planar vector fields and Hilbert's sixteenth problem
    • Birkhäuser, Verlag, Basel
    • R. Roussarie, Bifurcation of planar vector fields and Hilbert's sixteenth problem, Progress in Mathematics, Vol. 164, Birkhäuser, Verlag, Basel, 1998.
    • (1998) Progress in Mathematics , vol.164
    • Roussarie, R.1
  • 27
    • 0001012446 scopus 로고
    • A concrete example of the existence of four limit cycles for plane quadratic systems
    • Songling Shi A concrete example of the existence of four limit cycles for plane quadratic systems Sci. Sinica 23 1980 153-158
    • (1980) Sci. Sinica , vol.23 , pp. 153-158
    • Shi, S.1
  • 28
    • 49049152726 scopus 로고
    • A method of constructing cycles without contact around a weak focus
    • Songling Shi A method of constructing cycles without contact around a weak focus J. Differential Equations 41 1981 301-312
    • (1981) J. Differential Equations , vol.41 , pp. 301-312
    • Shi, S.1
  • 29
    • 0012776986 scopus 로고
    • On the structure of Poincaré-Lyapunov constants for the weak focus of polynomial vector fields
    • Songling Shi On the structure of Poincaré-Lyapunov constants for the weak focus of polynomial vector fields J. Differential Equations 52 1984 52-57
    • (1984) J. Differential Equations , vol.52 , pp. 52-57
    • Shi, S.1
  • 31
    • 0000113158 scopus 로고
    • Eleven small limit cycles in a cubic vector field
    • Zoła̧dek H. Eleven small limit cycles in a cubic vector field Nonlinearity 8 1995 843-860
    • (1995) Nonlinearity , vol.8 , pp. 843-860
    • Zoła̧dek, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.