메뉴 건너뛰기




Volumn 218, Issue 2, 2005, Pages 343-355

A family of isochronous foci with darboux first integral

Author keywords

Algebraic limit cycle; Center; Focus; Integrability

Indexed keywords


EID: 18844385952     PISSN: 00308730     EISSN: None     Source Type: Journal    
DOI: 10.2140/pjm.2005.218.343     Document Type: Article
Times cited : (18)

References (23)
  • 1
    • 0013028834 scopus 로고    scopus 로고
    • Integrability of cubic systems with degenerate infinity
    • [Chavarriga and Giné 1998]. MR 2001f:34052 Zbl 0998.34001
    • [Chavarriga and Giné 1998] J. Chavarriga and J. Giné, "Integrability of cubic systems with degenerate infinity", Differential Equations Dynam. Systems 6:4 (1998), 425-438. MR 2001f:34052 Zbl 0998.34001
    • (1998) Differential Equations Dynam. Systems , vol.6 , Issue.4 , pp. 425-438
    • Chavarriga, J.1    Giné, J.2
  • 2
    • 0033196213 scopus 로고    scopus 로고
    • On the integrability of two-dimensional flows
    • [Chavarriga et al. 1999]. MR 2000h:37058 Zbl 0940.37005
    • [Chavarriga et al. 1999] J. Chavarriga, H. Giacomini, J. Giné, and J. Llibre, "On the integrability of two-dimensional flows", J. Differential Equations 157:1 (1999), 163-182. MR 2000h:37058 Zbl 0940.37005
    • (1999) J. Differential Equations , vol.157 , Issue.1 , pp. 163-182
    • Chavarriga, J.1    Giacomini, H.2    Giné, J.3    Llibre, J.4
  • 3
    • 0035632529 scopus 로고    scopus 로고
    • On integrability of differential equations defined by the sum of homogeneous vector fields with degenerate infinity
    • [Chavarriga et al. 2001]. MR 2002g:34062
    • [Chavarriga et al. 2001] J. Chavarriga, I. A. García, and J. Giné, "On integrability of differential equations defined by the sum of homogeneous vector fields with degenerate infinity", Internat. J. Bifur. Chaos Appl. Sci. Engrg. 11:3 (2001), 711-722. MR 2002g:34062
    • (2001) Internat. J. Bifur. Chaos Appl. Sci. Engrg. , vol.11 , Issue.3 , pp. 711-722
    • Chavarriga, J.1    García, I.A.2    Giné, J.3
  • 4
    • 0037687358 scopus 로고    scopus 로고
    • An Abel ordinary differential equation class generalizing known integrable classes
    • [Cheb-Terrab and Roche 2003]. MR 2004c:34003 Zbl 1046.34004
    • [Cheb-Terrab and Roche 2003] E. S. Cheb-Terrab and A. D. Roche, "An Abel ordinary differential equation class generalizing known integrable classes", European J. Appl. Math. 14:2 (2003), 217-229. MR 2004c:34003 Zbl 1046.34004
    • (2003) European J. Appl. Math. , vol.14 , Issue.2 , pp. 217-229
    • Cheb-Terrab, E.S.1    Roche, A.D.2
  • 5
    • 85032069709 scopus 로고
    • Invariant algebraic curves and conditions for a centre
    • [Christopher 1994]. MR 95m:34052 Zbl 0821.34023
    • [Christopher 1994] C. J. Christopher, "Invariant algebraic curves and conditions for a centre", Proc. Roy. Soc. Edinburgh Sect. A 124:6 (1994), 1209-1229. MR 95m:34052 Zbl 0821.34023
    • (1994) Proc. Roy. Soc. Edinburgh Sect. A , vol.124 , Issue.6 , pp. 1209-1229
    • Christopher, C.J.1
  • 6
    • 0001870683 scopus 로고    scopus 로고
    • Integrability via invariant algebraic curves for planar polynomial differential systems
    • [Christopher and Llibre 2000]. MR 2001g:34001 Zbl 0974.34005
    • [Christopher and Llibre 2000] C. Christopher and J. Llibre, "Integrability via invariant algebraic curves for planar polynomial differential systems", Ann. Differential Equations 16:1 (2000), 5-19. MR 2001g:34001 Zbl 0974.34005
    • (2000) Ann. Differential Equations , vol.16 , Issue.1 , pp. 5-19
    • Christopher, C.1    Llibre, J.2
  • 7
    • 0001132390 scopus 로고    scopus 로고
    • Conditions for a centre in a simple class of cubic systems
    • [Collins 1997]. MR 98c:34043 Zbl 0894.34022
    • [Collins 1997] C. B. Collins, "Conditions for a centre in a simple class of cubic systems", Differential Integral Equations 10:2 (1997), 333-356. MR 98c:34043 Zbl 0894.34022
    • (1997) Differential Integral Equations , vol.10 , Issue.2 , pp. 333-356
    • Collins, C.B.1
  • 8
    • 0002809127 scopus 로고    scopus 로고
    • 2
    • [Conti 1994] edited by K. D. Elworthy et al., Lecture Notes in Pure and Appl. Math., Dekker, New York, 1994. MR 94i:34061 Zbl 0795.34021
    • 2", pp. 21-31 in Differential equations, dynamical systems, and control science, edited by K. D. Elworthy et al., Lecture Notes in Pure and Appl. Math. 152, Dekker, New York, 1994. MR 94i:34061 Zbl 0795.34021
    • Differential Equations, Dynamical Systems, and Control Science , vol.152 , pp. 21-31
    • Conti, R.1
  • 9
    • 0041801792 scopus 로고
    • The canonical integral in the neighborhood of a focus
    • [Dolov 1976]
    • [Dolov 1976] M. V. Dolov, "The canonical integral in the neighborhood of a focus", Differencial'nye Uravnenija 12:11 (1976), 1946-1953.
    • (1976) Differencial'nye Uravnenija , vol.12 , Issue.11 , pp. 1946-1953
    • Dolov, M.V.1
  • 10
    • 85039394561 scopus 로고
    • English translation. MR 56 #738 Zbl 0376.34004
    • English translation: Differential Equations 12 (1977), 1362-1368. MR 56 #738 Zbl 0376.34004
    • (1977) Differential Equations , vol.12 , pp. 1362-1368
  • 11
    • 0000128365 scopus 로고
    • Limit cycles for a class of Abel equations
    • [Gasull and Llibre 1990]. MR 91e:34036 Zbl 0732.34025
    • [Gasull and Llibre 1990] A. Gasull and J. Llibre, "Limit cycles for a class of Abel equations", SIAM J. Math. Anal. 21:5 (1990), 1235-1244. MR 91e:34036 Zbl 0732.34025
    • (1990) SIAM J. Math. Anal. , vol.21 , Issue.5 , pp. 1235-1244
    • Gasull, A.1    Llibre, J.2
  • 12
    • 0000763063 scopus 로고    scopus 로고
    • On the nonexistence, existence and uniqueness of limit cycles
    • [Giacomini et al. 1996]. MR 97a:34073 Zbl 0886.58087
    • [Giacomini et al. 1996] H. Giacomini, J. Llibre, and M. Viano, "On the nonexistence, existence and uniqueness of limit cycles", Nonlinearity 9:2 (1996), 501-516. MR 97a:34073 Zbl 0886.58087
    • (1996) Nonlinearity , vol.9 , Issue.2 , pp. 501-516
    • Giacomini, H.1    Llibre, J.2    Viano, M.3
  • 13
    • 1042291528 scopus 로고    scopus 로고
    • Integrability and algebraic limit cycles for polynomial differential systems with homogeneous nonlinearities
    • [Giné and Llibre 2004]. MR2004j:34077
    • [Giné and Llibre 2004] J. Giné and J. Llibre, "Integrability and algebraic limit cycles for polynomial differential systems with homogeneous nonlinearities", J. Differential Equations 197:1 (2004), 147-161. MR2004j:34077
    • (2004) J. Differential Equations , vol.197 , Issue.1 , pp. 147-161
    • Giné, J.1    Llibre, J.2
  • 14
    • 0010569308 scopus 로고    scopus 로고
    • On the Poincaré-Lyapunov constants and the Poincaré series
    • [Giné and Santallusia 2001]. MR 2002c:34044 Zbl 1022.34028
    • [Giné and Santallusia 2001] J. Giné and X. Santallusia, "On the Poincaré-Lyapunov constants and the Poincaré series", Appl. Math. (Warsaw) 28:1 (2001), 17-30. MR 2002c:34044 Zbl 1022.34028
    • (2001) Appl. Math. (Warsaw) , vol.28 , Issue.1 , pp. 17-30
    • Giné, J.1    Santallusia, X.2
  • 15
    • 85039394519 scopus 로고
    • [Kamke 1943] Mathematik und ihre Anwendungen, Becker & Erler, Leipzig. Zbl 0028.22702
    • [Kamke 1943] E. Kamke, Differentialgleichungen: Lösungsmethoden und Lösungen, Mathematik und ihre Anwendungen 18, Becker & Erler, Leipzig, 1943. Zbl 0028.22702
    • (1943) Differentialgleichungen: Lösungsmethoden und Lösungen , vol.18
    • Kamke, E.1
  • 16
    • 0002342437 scopus 로고
    • Algebraic invariant curves and the integrability of polynomial systems
    • [Kooij and Christopher 1993]. MR 1348232 Zbl 0784.34008
    • [Kooij and Christopher 1993] R. E. Kooij and C. J. Christopher, "Algebraic invariant curves and the integrability of polynomial systems", Applied Math. Letters 6:4 (1993), 51-53. MR 1348232 Zbl 0784.34008
    • (1993) Applied Math. Letters , vol.6 , Issue.4 , pp. 51-53
    • Kooij, R.E.1    Christopher, C.J.2
  • 17
    • 12144290753 scopus 로고    scopus 로고
    • Configurations of limit cycles and planar polynomial vector fields
    • [Llibre and Rodriguez 2004]. MR 2004j:34100
    • [Llibre and Rodriguez 2004] J. Llibre and G. Rodriguez, "Configurations of limit cycles and planar polynomial vector fields", J. Differential Equations 198:2 (2004), 374-380. MR 2004j:34100
    • (2004) J. Differential Equations , vol.198 , Issue.2 , pp. 374-380
    • Llibre, J.1    Rodriguez, G.2
  • 19
    • 0030396364 scopus 로고    scopus 로고
    • Algorithmic derivation of centre conditions
    • [Pearson et al. 1996]. MR 98c:34050 Zbl 0876.34033
    • [Pearson et al. 1996] J. M. Pearson, N. G. Lloyd, and C. J. Christopher, "Algorithmic derivation of centre conditions", SIAM Rev. 38:4 (1996), 619-636. MR 98c:34050 Zbl 0876.34033
    • (1996) SIAM Rev. , vol.38 , Issue.4 , pp. 619-636
    • Pearson, J.M.1    Lloyd, N.G.2    Christopher, C.J.3
  • 20
    • 0003654489 scopus 로고
    • [Petit Bois 1961] Dover, New York,. MR23#A256 Zbl 0098.26408
    • [Petit Bois 1961] G. Petit Bois, Tables ofindefinite integrals, Dover, New York, 1961. MR23#A256 Zbl 0098.26408
    • (1961) Tables Ofindefinite Integrals
    • Petit Bois, G.1
  • 21
    • 0001304970 scopus 로고
    • Algebraic and geometric aspects of the theory of polynomial vector fields
    • [Schlomiuk 1993] Montreal, PQ, edited by D. Schlomiuk, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., Kluwer Acad. Publ., Dordrecht, 1993. MR 95a:34042 Zbl 0790.34031
    • [Schlomiuk 1993] D. Schlomiuk, "Algebraic and geometric aspects of the theory of polynomial vector fields", pp. 429-467 in Bifurcations and periodic orbits of vector fields (Montreal, PQ, 1992), edited by D. Schlomiuk, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci. 408, Kluwer Acad. Publ., Dordrecht, 1993. MR 95a:34042 Zbl 0790.34031
    • (1992) Bifurcations and Periodic Orbits of Vector Fields , vol.408 , pp. 429-467
    • Schlomiuk, D.1
  • 22
    • 84968484573 scopus 로고
    • Liouvillian first integrals of differential equations
    • [Singer 1992]. MR 92m:12014 Zbl 0756.12006
    • [Singer 1992] M. F. Singer, "Liouvillian first integrals of differential equations", Trans. Amer. Math. Soc. 333:2 (1992), 673-688. MR 92m:12014 Zbl 0756.12006
    • (1992) Trans. Amer. Math. Soc. , vol.333 , Issue.2 , pp. 673-688
    • Singer, M.F.1
  • 23
    • 3042639874 scopus 로고    scopus 로고
    • Center conditions for a simple class of quintic systems
    • [Volokitin 2002]. MR 2002m:34042 Zbl 1008.34023
    • [Volokitin 2002] E. P. Volokitin, "Center conditions for a simple class of quintic systems", Int. J. Math. Math. Sci. 29:11 (2002), 625-632. MR 2002m:34042 Zbl 1008.34023
    • (2002) Int. J. Math. Math. Sci. , vol.29 , Issue.11 , pp. 625-632
    • Volokitin, E.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.