메뉴 건너뛰기




Volumn 47, Issue 10, 2012, Pages 1140-1153

Symbolic computation and the cyclicity problem for singularities

Author keywords

Bautin ideal; Computational commutative algebra; Cyclicity problem; Polynomial systems of nonlinear differential equations

Indexed keywords


EID: 84861531577     PISSN: 07477171     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jsc.2011.12.037     Document Type: Article
Times cited : (5)

References (24)
  • 1
    • 0011390657 scopus 로고
    • An Introduction to Gröbner Bases
    • American Mathematical Society, Providence, RI
    • Adams W.W., Loustaunau P. An Introduction to Gröbner Bases. Graduate Studies in Mathematics 1994, vol. 3. American Mathematical Society, Providence, RI.
    • (1994) Graduate Studies in Mathematics , vol.3
    • Adams, W.W.1    Loustaunau, P.2
  • 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. Sbornik N.S.. Trans. Amer. Math. Soc. 1954, 100:181-196.
    • (1954) Mat. Sbornik N.S.. Trans. Amer. Math. Soc. , vol.100 , pp. 181-196
    • Bautin, N.N.1
  • 5
    • 79951557461 scopus 로고    scopus 로고
    • Singular 3-2-1. A Computer Algebra System for Polynomial Computations
    • Centre for Computer Algebra, University of Kaiserslautern.
    • Decker, W., Greuel, G.-M., Pfister, G., Schönemann, H., (2010). Singular 3-2-1. A Computer Algebra System for Polynomial Computations. Centre for Computer Algebra, University of Kaiserslautern. http://www.singular.uni-kl.de.
    • (2010)
    • Decker, W.1    Greuel, G.-M.2    Pfister, G.3    Schönemann, H.4
  • 6
    • 57449116731 scopus 로고    scopus 로고
    • primdec.lib A Singular 3-1-2 library for computing the primary decomposition and radical of ideals
    • Decker, W., Laplagne, S., Pfister, G., Schönemann, H.A., (2010). primdec.lib A Singular 3-1-2 library for computing the primary decomposition and radical of ideals.
    • (2010)
    • Decker, W.1    Laplagne, S.2    Pfister, G.3    Schönemann, H.A.4
  • 7
    • 0000173117 scopus 로고
    • Détermination et intégration d'une certaine classe d'équations différentielles ayant pour point singulier un centre
    • Dulac H. Détermination et intégration d'une certaine classe d'équations différentielles ayant pour point singulier un centre. Bull. Sci. Math. 1908, 32(2):230-252.
    • (1908) Bull. Sci. Math. , vol.32 , Issue.2 , pp. 230-252
    • Dulac, H.1
  • 8
    • 33748423721 scopus 로고    scopus 로고
    • On some open problems in planar differential systems and Hilbert's 16th problem
    • Giné J. On some open problems in planar differential systems and Hilbert's 16th problem. Chaos Solitons Fractals 2007, 31:1118-1134.
    • (2007) Chaos Solitons Fractals , vol.31 , pp. 1118-1134
    • Giné, J.1
  • 11
    • 0035997405 scopus 로고    scopus 로고
    • Centennial history of Hilbert's 16th problem
    • Ilyashenko Yu. Centennial history of Hilbert's 16th problem. Bull. Amer. Math. Soc. (N.S.) 2002, 39:301-354.
    • (2002) Bull. Amer. Math. Soc. (N.S.) , vol.39 , pp. 301-354
    • Ilyashenko, Y.1
  • 12
    • 62949218081 scopus 로고    scopus 로고
    • Lectures on Analytic Differential Equations
    • American Mathematical Society, Providence
    • Ilyashenko Yu., Yakovenko S. Lectures on Analytic Differential Equations. Graduate Studies in Mathematics 2008, vol. 86. American Mathematical Society, Providence.
    • (2008) Graduate Studies in Mathematics , vol.86
    • Ilyashenko, Y.1    Yakovenko, S.2
  • 14
    • 0037246396 scopus 로고    scopus 로고
    • Hilbert's 16th problem and bifurcations of planar polynomial vector fields
    • Li J. Hilbert's 16th problem and bifurcations of planar polynomial vector fields. Internat. J. Bifur. Chaos Appl. Sci. Engrg. 2003, 13:47-106.
    • (2003) Internat. J. Bifur. Chaos Appl. Sci. Engrg. , vol.13 , pp. 47-106
    • Li, J.1
  • 15
    • 0001939637 scopus 로고
    • Theory of values of singular point in complex autonomous differential systems
    • Liu Y.-R., Li J.-B. Theory of values of singular point in complex autonomous differential systems. Sci. China Ser. A 1990, 33:10-23.
    • (1990) Sci. China Ser. A , vol.33 , pp. 10-23
    • Liu, Y.-R.1    Li, J.-B.2
  • 16
    • 55649103985 scopus 로고    scopus 로고
    • Computational algebra and limit cycle bifurcations in polynomial systems
    • Romanovski V.G. Computational algebra and limit cycle bifurcations in polynomial systems. Nonlinear Phenom. Complex Syst. 2007, 10:79-85.
    • (2007) Nonlinear Phenom. Complex Syst. , vol.10 , pp. 79-85
    • Romanovski, V.G.1
  • 17
    • 79958772293 scopus 로고    scopus 로고
    • Time-Reversibility in 2-Dim Systems
    • Romanovski V.G. Time-Reversibility in 2-Dim Systems. Open Syst. Inf. Dyn. 2008, 15:359-370.
    • (2008) Open Syst. Inf. Dyn. , vol.15 , pp. 359-370
    • Romanovski, V.G.1
  • 18
    • 0035976829 scopus 로고    scopus 로고
    • The center and isochronicity problems for some cubic systems
    • Romanovski V.G., Robnik M. The center and isochronicity problems for some cubic systems. J. Phys. A: Math. Gen. 2001, 34:10267-10292.
    • (2001) J. Phys. A: Math. Gen. , vol.34 , pp. 10267-10292
    • Romanovski, V.G.1    Robnik, M.2
  • 21
    • 0003244212 scopus 로고    scopus 로고
    • Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem
    • Birkhäuser, Basel
    • Roussarie R. Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem. Progress in Mathematics 1998, vol. 164. Birkhäuser, Basel.
    • (1998) Progress in Mathematics , vol.164
    • Roussarie, R.1
  • 22
    • 0003876590 scopus 로고
    • Introduction to the Algebraic Theory of Invariants of Differential Equations
    • Manchester University Press, Manchester
    • Sibirsky K.S. Introduction to the Algebraic Theory of Invariants of Differential Equations. Kishinev: Shtiintsa 1988, 1982. Manchester University Press, Manchester.
    • (1988) Kishinev: Shtiintsa , vol.1982
    • Sibirsky, K.S.1
  • 23
    • 0000187914 scopus 로고
    • A geometric proof of the Bautin theorem
    • Concerning the Hilbert Sixteenth Problem. Advances in Mathematical Sciences, vol. 23
    • Yakovenko S. A geometric proof of the Bautin theorem. Amer. Math. Soc. Transl. 1995, 165:203-219.
    • (1995) Amer. Math. Soc. Transl. , vol.165 , pp. 203-219
    • Yakovenko, S.1
  • 24
    • 0000813963 scopus 로고
    • Quadratic systems with center and their perturbations
    • Zoła̧dek H. Quadratic systems with center and their perturbations. J. Differential Equations 1994, 109:223-273.
    • (1994) J. Differential Equations , vol.109 , pp. 223-273
    • Zoła̧dek, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.