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Volumn 250, Issue 4, 2011, Pages 2162-2176

Classical Liénard equations of degree n≥6 can have [n-1/2]+2 limit cycles

Author keywords

Classical Li nard equations; Limit cycles; Relaxation oscillation; Singular perturbations; Slow fast system

Indexed keywords


EID: 78650982367     PISSN: 00220396     EISSN: 10902732     Source Type: Journal    
DOI: 10.1016/j.jde.2010.12.003     Document Type: Article
Times cited : (73)

References (14)
  • 1
    • 0003224933 scopus 로고    scopus 로고
    • Mathematical problems for the next century
    • Amer. Math. Soc., Providence, RI
    • Smale S. Mathematical problems for the next century. Mathematics: Frontiers and Perspectives 2000, 271-294. Amer. Math. Soc., Providence, RI.
    • (2000) Mathematics: Frontiers and Perspectives , pp. 271-294
    • Smale, S.1
  • 2
    • 0000923674 scopus 로고
    • On Liénard's equation
    • Springer, Berlin, Geometry and Topology, Proc. III Latin Amer. School of Math., Inst. Mat. Pura Aplicada CNPq
    • Lins A., de Melo W., Pugh C.C. On Liénard's equation. Lecture Notes in Math. 1977, vol. 597:335-357. Springer, Berlin.
    • (1977) Lecture Notes in Math. , vol.597 , pp. 335-357
    • Lins, A.1    de Melo, W.2    Pugh, C.C.3
  • 3
    • 84892361168 scopus 로고    scopus 로고
    • Qualitative Theory of Planar Differential Systems
    • Springer-Verlag, Berlin
    • Dumortier F., Llibre J., Artés J. Qualitative Theory of Planar Differential Systems. Universitext 2006, Springer-Verlag, Berlin.
    • (2006) Universitext
    • Dumortier, F.1    Llibre, J.2    Artés, J.3
  • 4
    • 34548864003 scopus 로고    scopus 로고
    • More limit cycles than expected in Liénard equations
    • (electronic)
    • Dumortier F., Panazzolo D., Roussarie R. More limit cycles than expected in Liénard equations. Proc. Amer. Math. Soc. 2007, 135(6):1895-1904. (electronic). http://dx.doi.org/10.1090/S0002-9939-07-08688-1, 10.1090/S0002-9939-07-08688-1.
    • (2007) Proc. Amer. Math. Soc. , vol.135 , Issue.6 , pp. 1895-1904
    • Dumortier, F.1    Panazzolo, D.2    Roussarie, R.3
  • 5
    • 33847738659 scopus 로고    scopus 로고
    • Putting a boundary to the space of Liénard equations
    • Roussarie R. Putting a boundary to the space of Liénard equations. Discrete Contin. Dyn. Syst. 2007, 17(2):441-448.
    • (2007) Discrete Contin. Dyn. Syst. , vol.17 , Issue.2 , pp. 441-448
    • Roussarie, R.1
  • 6
    • 33646111687 scopus 로고    scopus 로고
    • Compactification and desingularization of spaces of polynomial Liénard equations
    • Dumortier F. Compactification and desingularization of spaces of polynomial Liénard equations. J. Differential Equations 2006, 224(2):296-313. http://dx.doi.org/10.1016/j.jde.2005.08.011, 10.1016/j.jde.2005.08.011.
    • (2006) J. Differential Equations , vol.224 , Issue.2 , pp. 296-313
    • Dumortier, F.1
  • 7
    • 0030136548 scopus 로고    scopus 로고
    • Canard cycles and center manifolds
    • x+100, with an appendix by Li Chengzhi
    • Dumortier F., Roussarie R. Canard cycles and center manifolds. Mem. Amer. Math. Soc. 1996, 121(577). x+100, with an appendix by Li Chengzhi.
    • (1996) Mem. Amer. Math. Soc. , vol.121 , Issue.577
    • Dumortier, F.1    Roussarie, R.2
  • 8
    • 79952182938 scopus 로고    scopus 로고
    • Bifurcations of multiple relaxation oscillations in polynomial Liénard equations, Proc. Amer. Math. Soc., doi:, in press. doi:10.1090/S0002-9939-2010-10610-X
    • P. De Maesschalck, F. Dumortier, Bifurcations of multiple relaxation oscillations in polynomial Liénard equations, Proc. Amer. Math. Soc., doi:, in press. doi:10.1090/S0002-9939-2010-10610-X.
    • De Maesschalck, P.1    Dumortier, F.2
  • 9
    • 0033586174 scopus 로고    scopus 로고
    • Polynomial Liénard equations near infinity
    • Dumortier F., Herssens C. Polynomial Liénard equations near infinity. J. Differential Equations 1999, 153(1):1-29.
    • (1999) J. Differential Equations , vol.153 , Issue.1 , pp. 1-29
    • Dumortier, F.1    Herssens, C.2
  • 10
    • 78650995980 scopus 로고    scopus 로고
    • Slow divergence integral and balanced canard solutions, Qual. Theory Dyn. Syst., in press.
    • F. Dumortier, Slow divergence integral and balanced canard solutions, Qual. Theory Dyn. Syst., in press.
    • Dumortier, F.1
  • 11
    • 18144396577 scopus 로고    scopus 로고
    • Time analysis and entry-exit relation near planar turning points
    • De Maesschalck P., Dumortier F. Time analysis and entry-exit relation near planar turning points. J. Differential Equations 2005, 215(2):225-267. http://dx.doi.org/10.1016/j.jde.2005.01.004, 10.1016/j.jde.2005.01.004.
    • (2005) J. Differential Equations , vol.215 , Issue.2 , pp. 225-267
    • De Maesschalck, P.1    Dumortier, F.2
  • 12
    • 78149469573 scopus 로고    scopus 로고
    • Birth of canard cycles
    • Dumortier F., Roussarie R. Birth of canard cycles. Discrete Contin. Dyn. Syst. Ser. S 2009, 2(4):723-781. http://dx.doi.org/10.3934/dcdss.2009.2.723, 10.3934/dcdss.2009.2.723.
    • (2009) Discrete Contin. Dyn. Syst. Ser. S , vol.2 , Issue.4 , pp. 723-781
    • Dumortier, F.1    Roussarie, R.2
  • 14
    • 0034859064 scopus 로고    scopus 로고
    • Algorithms for quad-double precision floating point arithmetic
    • IEEE Comput. Soc.
    • Hida Y., Li X.S., Bailey D.H. Algorithms for quad-double precision floating point arithmetic. 15th IEEE Symposium on Computer Arithmetic 2001, 155-162. IEEE Comput. Soc.
    • (2001) 15th IEEE Symposium on Computer Arithmetic , pp. 155-162
    • Hida, Y.1    Li, X.S.2    Bailey, D.H.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.