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Volumn 24, Issue 2, 2005, Pages 491-499

Resolution of the Poincaré problem and nonexistence of algebraic limit cycles in family (I) of Chinese classification

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; EIGENVALUES AND EIGENFUNCTIONS; MATHEMATICAL MODELS; MATRIX ALGEBRA; POLYNOMIALS; QUADRATIC PROGRAMMING; THEOREM PROVING; VECTORS;

EID: 10844283489     PISSN: 09600779     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.chaos.2004.06.076     Document Type: Article
Times cited : (5)

References (14)
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    • Algebraic limit cycles of degree 4 for quadratic systems
    • Chavarriga J, Llibre J, Sorolla J. Algebraic limit cycles of degree 4 for quadratic systems. J Different Equal 2004;200:206-44.
    • (2004) J Different Equal , vol.200 , pp. 206-244
    • Chavarriga, J.1    Llibre, J.2    Sorolla, J.3
  • 4
    • 0003136372 scopus 로고
    • Mémoire sur les équations différentielles algebriques du premier ordre et du premier degré (Mélanges)
    • Darboux G. Mémoire sur les équations différentielles algebriques du premier ordre et du premier degré (Mélanges). Bull Sci Math 1878;32:60-96. 123-144; 151-200.
    • (1878) Bull Sci Math , vol.32 , pp. 60-96
    • Darboux, G.1
  • 5
    • 10844254158 scopus 로고    scopus 로고
    • Transcendental limit cycles via the structure of arbitrary degree invariant algebraic curves of polynomial planar vector fields
    • [in press]
    • Garcia IA. Transcendental limit cycles via the structure of arbitrary degree invariant algebraic curves of polynomial planar vector fields. Rocky Mountain J Math [in press].
    • Rocky Mountain J Math
    • Garcia, I.A.1
  • 7
    • 0000876447 scopus 로고
    • The limit cycle of the van der Pol equation is not algebraic
    • Odani K. The limit cycle of the van der Pol equation is not algebraic. J Different Equat 1995;15:146-52.
    • (1995) J Different Equat , vol.15 , pp. 146-152
    • Odani, K.1
  • 8
    • 65749318814 scopus 로고
    • Sur l'integration algébrique des équations différentielles du premier ordre et du premier degré(I and II)
    • Poincaré H. Sur l'integration algébrique des équations différentielles du premier ordre et du premier degré(I and II). Rend cire mat Palermo 1891;5:161-91. [1897;11:193-239
    • (1891) Rend Cire Mat Palermo , vol.5 , pp. 161-191
    • Poincaré, H.1
  • 9
    • 0007074404 scopus 로고
    • Poincaré H. Sur l'integration algébrique des équations différentielles du premier ordre et du premier degré(I and II). Rend cire mat Palermo 1891;5:161-91. [1897;11:193-239
    • (1897) Rend Cire Mat Palermo , vol.11 , pp. 193-239
  • 11
    • 0000596681 scopus 로고
    • Reduction of singularities of the differential equation Ady = Bdx
    • Seidenberg A. Reduction of singularities of the differential equation Ady = Bdx. Am J Math 1968;90:248-69.
    • (1968) Am J Math , vol.90 , pp. 248-269
    • Seidenberg, A.1
  • 12
    • 0006296075 scopus 로고    scopus 로고
    • On the Poincaré problem
    • Watcher S. On the Poincaré problem. J Different Equat 2000;166:51-78.
    • (2000) J Different Equat , vol.166 , pp. 51-78
    • Watcher, S.1
  • 13
    • 0003264465 scopus 로고
    • Theory of limit cycles
    • Providence: American Mathematical Society
    • Ye Y-Q. In: Theory of limit cycles. Translations of Math Monographs, 66. Providence: American Mathematical Society; 1986.
    • (1986) Translations of Math Monographs , vol.66
    • Ye, Y.-Q.1
  • 14
    • 22044453607 scopus 로고    scopus 로고
    • Algebraic invariant curves for the Lienard equation
    • Zoła̧dek H. Algebraic invariant curves for the Lienard equation. Trans Am Math Soc 1998;350:1681-701.
    • (1998) Trans Am Math Soc , vol.350 , pp. 1681-1701
    • Zoła̧dek, H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.