메뉴 건너뛰기




Volumn 22, Issue 1, 2009, Pages 213-237

Horseshoes in the forced van der Pol system

Author keywords

[No Author keywords available]

Indexed keywords


EID: 58149392828     PISSN: 09517715     EISSN: 13616544     Source Type: Journal    
DOI: 10.1088/0951-7715/22/1/011     Document Type: Article
Times cited : (37)

References (38)
  • 3
    • 0001031806 scopus 로고
    • 3 et leurs canards
    • 3 et leurs canards Third Schnepfenried Geometry Conf. (Schnepfenried, France, 1982) (Astérisque vol 109) vol 2 (Paris: Soc. Math. France) pp 159-191
    • (1983) Third Schnepfenried Geometry Conf. , vol.2 , pp. 159-191
    • Benoît, I.1
  • 6
    • 0002430596 scopus 로고
    • Formal expansion of van der Pol equation canard solutions are Gevrey
    • Canalis-Durand M 1991 Formal expansion of van der Pol equation canard solutions are Gevrey Dynamic Bifurcations (Luminy, 1990) (Lecture Notes in Mathematics vol 1493) (Berlin: Springer) pp 29-39
    • (1991) Dynamic Bifurcations , vol.1493 , pp. 29-39
    • Canalis-Durand, M.1
  • 7
    • 0000386549 scopus 로고
    • On non-linear differential equations of the second order: I. the equation large
    • Cartwright M L and Littlewood J E 1945 On non-linear differential equations of the second order: I. The equation large J. Lond. Math. Soc. 20 180-9
    • (1945) J. Lond. Math. Soc. , vol.20 , pp. 180-189
    • Cartwright, M.L.1    Littlewood, J.E.2
  • 8
    • 0030136548 scopus 로고    scopus 로고
    • Canard cycles and center manifolds
    • Dumortier F and Roussarie R 1996 Canard cycles and center manifolds Mem. Amer. Math. Soc. 121 x+100 (with an appendix by Cheng Zhi Li)
    • (1996) Mem. Amer. Math. Soc. , vol.121 , pp. 100
    • Dumortier, F.1    Roussarie, R.2
  • 9
    • 0001356311 scopus 로고
    • Persistence and smoothness of invariant manifolds for flows
    • Fenichel N 1971/1972 Persistence and smoothness of invariant manifolds for flows Indiana Univ. Math. J. 21 193-226
    • (1971) Indiana Univ. Math. J. , vol.21 , Issue.3 , pp. 193-226
    • Fenichel, N.1
  • 10
    • 34250627892 scopus 로고
    • Geometric singular perturbation theory for ordinary differential equations
    • Fenichel N 1979 Geometric singular perturbation theory for ordinary differential equations J. Diff. Eqns 31 53-98
    • (1979) J. Diff. Eqns , vol.31 , Issue.1 , pp. 53-98
    • Fenichel, N.1
  • 12
    • 32544443856 scopus 로고
    • Phase portraits of planar vector fields: Computer proofs
    • Guckenheimer J 1995 Phase portraits of planar vector fields: computer proofs Exp. Math. 4 153-65
    • (1995) Exp. Math. , vol.4 , pp. 153-165
    • Guckenheimer, J.1
  • 14
    • 3042631914 scopus 로고    scopus 로고
    • The forced van der Pol equation: I. the slow flow and its bifurcations
    • Guckenheimer J, Hoffman K and Weckesser W 2003 The forced van der Pol equation: I. The slow flow and its bifurcations SIAM J. Appl. Dyn. Syst. 2 1-35 (electronic)
    • (2003) SIAM J. Appl. Dyn. Syst. , vol.2 , Issue.1 , pp. 1-35
    • Guckenheimer, J.1    Hoffman, K.2    Weckesser, W.3
  • 16
    • 58149375873 scopus 로고    scopus 로고
    • Haiduc R 2005 Horseshoes in the forced van der Pol equation PhD in Mathematics Cornell University, Ithaca, New York 14853
    • (2005) PhD in Mathematics
    • Haiduc, R.1
  • 17
    • 58149385635 scopus 로고    scopus 로고
    • Hargreaves G I 2002 Interval analysis in MATLAB Numerical Analysis Report No 416 Manchester Centre for Computational Mathematics, Manchester, England http://www.maths.man.ac.uk/ nareports/narep416.pdf
    • (2002) Numerical Analysis Report No 416
    • Hargreaves, G.I.1
  • 18
    • 58149377719 scopus 로고    scopus 로고
    • Ilyashenko Yu and Li W 1999 Nonlocal Bifurcations (Mathematical Surveys and Monographs vol 66) (Providence, RI: American Mathematical Society)
    • (1999) Nonlocal Bifurcations
    • Yu, I.1    Li, W.2
  • 19
    • 58149373973 scopus 로고    scopus 로고
    • INTEGRO http://www.cam.cornell.edu/∼roj/odetools/
    • Integro1
  • 20
    • 58149380133 scopus 로고    scopus 로고
    • INTLAB http://www.ti3.tu-harburg.de/∼rump/intlab/
    • Intlab1
  • 21
    • 0002316532 scopus 로고
    • Geometric singular perturbation theory
    • Jones C K R T 1995 Geometric singular perturbation theory Dynamical Systems (Montecatini Terme, 1994) (Lecture Notes in Mathematics vol 1609) (Berlin: Springer) pp 44-118
    • (1995) Dynamical Systems , vol.1609 , pp. 44-118
    • Jones, C.K.R.T.1
  • 22
    • 0002887375 scopus 로고
    • Qualitative analysis of the periodically forced relaxation oscillations
    • Levi M 1981 Qualitative analysis of the periodically forced relaxation oscillations Mem. Am. Math. Soc. 32 vi+147
    • (1981) Mem. Am. Math. Soc. , vol.32 , pp. 147
    • Levi, M.1
  • 23
    • 0000057066 scopus 로고
    • A second order differential equation with singular solutions
    • Levinson N 1949 A second order differential equation with singular solutions Ann. Math. (2) 50 127-53
    • (1949) Ann. Math. (2) , vol.50 , Issue.1 , pp. 127-153
    • Levinson, N.1
  • 26
    • 0003588811 scopus 로고    scopus 로고
    • Moser J 2001 Stable and Random Motions in Dynamical Systems (Princeton Landmarks in Mathematics) (Princeton, NJ: Princeton University Press) (with special emphasis on celestial mechanics, reprint of the 1973 original, with a foreword by Philip J Holmes)
    • (2001) Stable and Random Motions in Dynamical Systems
    • Moser, J.1
  • 27
    • 0000839621 scopus 로고
    • A structural stability theorem
    • Robbin J W 1971 A structural stability theorem Ann. Math. (2) 94 447-93
    • (1971) Ann. Math. (2) , vol.94 , Issue.3 , pp. 447-493
    • Robbin, J.W.1
  • 29
    • 58149401837 scopus 로고    scopus 로고
    • Rump S M 1999 Intlab-Interval Laboratory http://www.ti3.tu-harburg.de/ publications/Intlab.ps.gz
    • (1999)
    • Rump, S.M.1
  • 30
    • 0002737270 scopus 로고
    • Diffeomorphisms with many periodic points
    • Smale S 1965 Diffeomorphisms with many periodic points Differential and Combinatorial Topology (A Symposium in Honor of Marston Morse) (Princeton, NJ: Princeton University Press) pp 63-80
    • (1965) Differential and Combinatorial Topology , pp. 63-80
    • Smale, S.1
  • 31
    • 21944453346 scopus 로고    scopus 로고
    • Finding a horseshoe on the beaches of Rio
    • Smale S 1998 Finding a horseshoe on the beaches of Rio Math. Intelligencer 20 39-44
    • (1998) Math. Intelligencer , vol.20 , pp. 39-44
    • Smale, S.1
  • 35
    • 0000873906 scopus 로고
    • On 'relaxation oscillations' i
    • van der Pol B 1926 On 'relaxation oscillations' I Phil. Mag. 2 978-92
    • (1926) Phil. Mag. , vol.2 , pp. 978-992
    • Van Der Pol, B.1
  • 36
    • 30244449696 scopus 로고
    • Frequency demultiplication
    • van der Pol B and van der Mark J 1927 Frequency demultiplication Nature 120 363-4
    • (1927) Nature , vol.120 , Issue.3019 , pp. 363-364
    • Van Der Pol, B.1    Van Der Mark, J.2
  • 37
    • 0000401026 scopus 로고
    • The heartbeat considered as a relaxation oscillation, and an electrical model of the heart
    • van der Pol B and van der Mark J 1928 The heartbeat considered as a relaxation oscillation, and an electrical model of the heart Phil. Mag. Suppl. 6 763-75
    • (1928) Phil. Mag. Suppl. , vol.6 , pp. 763-775
    • Van Der Pol, B.1    Van Der Mark, J.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.