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Proceedings of the American Mathematical Society
Volumn 139, Issue 6, 2011, Pages 2073-2085
Bifurcations of multiple relaxation oscillations in polynomial liénard equations
Author keywords

Elementary catastrophy; Limit cycles; Polynomial Li nard equations; Relaxation oscillation; Singular perturbations; Slow fast system
Indexed keywords

EID: 79952182938     PISSN: 00029939     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9939-2010-10610-X     Document Type: Article
Times cited : (13)
References (8)
  • 1
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    • (2008) Proc. Roy. Soc. Edinburgh Sect. A , vol.138 , Issue.2 , pp. 265-299
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  • 2
    • 34548864003 scopus 로고    scopus 로고
    • More limit cycles than expected in Liénard equations
    • (electronic). MR2286102 (2007m:34081)
    • [DPR07] Freddy Dumortier, Daniel Panazzolo, and Robert Roussarie, More limit cycles than expected in Liénard equations, Proc. Amer. Math. Soc. 135 (2007), no. 6, 1895-1904 (electronic). MR2286102 (2007m:34081)
    • (2007) Proc. Amer. Math. Soc. , vol.135 , Issue.6 , pp. 1895-1904
    • Dumortier, F.1    Panazzolo, D.2    Roussarie, R.3
  • 3
    • 0035920091 scopus 로고    scopus 로고
    • Multiple canard cycles in generalized Liénard equations
    • DOI 10.1006/jdeq.2000.3947, PII S0022039600939470
    • [DR01] F. Dumortier and R. Roussarie, Multiple canard cycles in generalized Liénard equations, J. Differential Equations 174 (2001), no. 1, 1-29. MR1844521 (2002k:34076) (Pubitemid 33378036)
    • (2001) Journal of Differential Equations , vol.174 , Issue.1 , pp. 1-29
    • Dumortier, F.1    Roussarie, R.2
  • 4
    • 39649084400 scopus 로고    scopus 로고
    • Bifurcation of relaxation oscillations in dimension two
    • MR2342266 (2008k:34164)
    • [DR07] Freddy Dumortier and Robert Roussarie, Bifurcation of relaxation oscillations in dimension two, Discrete Contin. Dyn. Syst. 19 (2007), no. 4, 631-674. MR2342266 (2008k:34164)
    • (2007) Discrete Contin. Dyn. Syst. , vol.19 , Issue.4 , pp. 631-674
    • Dumortier, F.1    Roussarie, R.2
  • 6
    • 0003220351 scopus 로고
    • Stable mappings and their singularities
    • Springer-Verlag, New York, MR0341518 (49:6269)
    • [GG73] M. Golubitsky and V. Guillemin, Stable mappings and their singularities, Graduate Texts in Mathematics, Vol. 14, Springer-Verlag, New York, 1973. MR0341518 (49:6269)
    • (1973) Graduate Texts in Mathematics , vol.14
    • Golubitsky, M.1    Guillemin, V.2
  • 7
    • 0000923674 scopus 로고
    • On liénard's equation
    • Geometry and topology (Proc. III Latin Amer. School of Math., Inst. Mat. Pura Aplicada CNPq, Rio de Janeiro, Springer, Berlin, MR0448423 (56:6730)
    • [LdMP77] A. Lins, W. de Melo, and C. C. Pugh, On Liénard's equation, Geometry and topology (Proc. III Latin Amer. School of Math., Inst. Mat. Pura Aplicada CNPq, Rio de Janeiro, 1976), Lecture Notes in Math., Vol. 597, Springer, Berlin, 1977, pp. 335-357. MR0448423 (56:6730)
    • (1976) Lecture Notes in Math. , vol.597 , Issue.1977 , pp. 335-357
    • Lins, A.1    De Melo, W.2    Pugh, C.C.3
  • 8
    • 33847738659 scopus 로고    scopus 로고
    • Putting a boundary to the space of liénard equations
    • MR2257444 (2007i:34046)
    • [Rou07] R. Roussarie, Putting a boundary to the space of Liénard equations, Discrete Contin. Dyn. Syst. 17 (2007), no. 2, 441-448. MR2257444 (2007i:34046)
    • (2007) Discrete Contin. Dyn. Syst. , vol.17 , Issue.2 , pp. 441-448
    • Roussarie, R.1

* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.