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Volumn 7, Issue 3, 2008, Pages 712-754

Tangency bifurcations of global poincaré maps

Author keywords

Flowbox; Normal forms; Poincar map; Quadratic and cubic tangency; Singularity theory

Indexed keywords

BIFURCATION (MATHEMATICS); CIRCUIT OSCILLATIONS; KETONES; LASERS; OPTICAL PROJECTORS; ORBITS; SEMICONDUCTOR DEVICE MODELS; SEMICONDUCTOR LASERS; SEMICONDUCTOR MATERIALS; TIME VARYING SYSTEMS; VECTORS;

EID: 54949085160     PISSN: None     EISSN: 15360040     Source Type: Journal    
DOI: 10.1137/07069972X     Document Type: Article
Times cited : (26)

References (46)
  • 2
  • 3
    • 0000024406 scopus 로고
    • Dynamical systems with two degrees of freedom
    • G. D. BIRKHOFF, Dynamical systems with two degrees of freedom, Trans. Amer. Math. Soc., 18 (1917), pp. 199-300.
    • (1917) Trans. Amer. Math. Soc , vol.18 , pp. 199-300
    • BIRKHOFF, G.D.1
  • 5
    • 55849134899 scopus 로고
    • Topological equivalence of diffeomorphisms and curves
    • C. BONATTI AND M. A. TEIXEIRA, Topological equivalence of diffeomorphisms and curves, J. Differential Equations, 118 (1995), pp. 371-379.
    • (1995) J. Differential Equations , vol.118 , pp. 371-379
    • BONATTI, C.1    TEIXEIRA, M.A.2
  • 7
    • 0037032874 scopus 로고    scopus 로고
    • A note on diffeomorphism and periodic differential equations
    • W.-C. C. CHAN, A note on diffeomorphism and periodic differential equations, Math. Comput. Modelling, 36 (2002), pp. 1387-1392.
    • (2002) Math. Comput. Modelling , vol.36 , pp. 1387-1392
    • CHAN, W.-C.C.1
  • 8
    • 84960604768 scopus 로고
    • Analytic quasi-periodic curves of discontinuous type on a torus
    • T. M. CHERRY, Analytic quasi-periodic curves of discontinuous type on a torus, Proc. London Math. Soc. (2), 44 (1938), pp. 175-215.
    • (1938) Proc. London Math. Soc. (2) , vol.44 , pp. 175-215
    • CHERRY, T.M.1
  • 9
    • 0036936115 scopus 로고    scopus 로고
    • Discontinuity geometry for an impact oscillator
    • D. R. J. CHILLINGWORTH, Discontinuity geometry for an impact oscillator, Dyn. Syst., 17 (2002), pp. 389-420.
    • (2002) Dyn. Syst , vol.17 , pp. 389-420
    • CHILLINGWORTH, D.R.J.1
  • 10
    • 41349084180 scopus 로고    scopus 로고
    • Entropy and bifurcations in a chaotic laser
    • P. COLLINS AND B. KRAUSKOPF, Entropy and bifurcations in a chaotic laser, Phys. Rev. E (3), 66 (2002), 056201.
    • (2002) Phys. Rev. E , vol.66 , Issue.3 , pp. 056201
    • COLLINS, P.1    KRAUSKOPF, B.2
  • 11
    • 21844514948 scopus 로고
    • Complete Poincaré sections and tangent sets
    • H. R. DULLIN AND A. WITTEK, Complete Poincaré sections and tangent sets, J. Phys. A, 28 (1995), pp. 7157-7180.
    • (1995) J. Phys. A , vol.28 , pp. 7157-7180
    • DULLIN, H.R.1    WITTEK, A.2
  • 13
    • 33644887198 scopus 로고    scopus 로고
    • Computing one-dimensional global manifolds of Poincaré maps by continuation
    • J. P. ENGLAND, B. KRAUSKOPF, AND H. M. OSINGA, Computing one-dimensional global manifolds of Poincaré maps by continuation, SIAM J. Appl. Dyn. Syst., 4 (2005), pp. 1008-1041.
    • (2005) SIAM J. Appl. Dyn. Syst , vol.4 , pp. 1008-1041
    • ENGLAND, J.P.1    KRAUSKOPF, B.2    OSINGA, H.M.3
  • 14
    • 0032584576 scopus 로고    scopus 로고
    • Visualization of three-dimensional chaos
    • G. O. FOUNTAIN, D. V. KHAKHAR, AND J. M. OTTINO, Visualization of three-dimensional chaos, Science, 281 (1998), pp. 683-686.
    • (1998) Science , vol.281 , pp. 683-686
    • FOUNTAIN, G.O.1    KHAKHAR, D.V.2    OTTINO, J.M.3
  • 16
    • 37649030953 scopus 로고    scopus 로고
    • Global bifurcations and bistability at the locking boundaries of a semiconductor laser with phase-conjugate feedback
    • K. GREEN AND B. KRAUSKOPF, Global bifurcations and bistability at the locking boundaries of a semiconductor laser with phase-conjugate feedback, Phys. Rev. E (3), 66 (2002), 016220.
    • (2002) Phys. Rev. E , vol.66 , Issue.3 , pp. 016220
    • GREEN, K.1    KRAUSKOPF, B.2
  • 21
    • 30444443162 scopus 로고    scopus 로고
    • Canonically transformed detectors applied to the classical inverse scattering problem
    • C. JUNG, T. H. SELIGMAN, AND J. M. TORRES, Canonically transformed detectors applied to the classical inverse scattering problem, J. Nonlinear Math. Phys., 12 (2005), pp. 404-411.
    • (2005) J. Nonlinear Math. Phys , vol.12 , pp. 404-411
    • JUNG, C.1    SELIGMAN, T.H.2    TORRES, J.M.3
  • 22
    • 0034645707 scopus 로고    scopus 로고
    • Some considerations on Poincaré maps for chaotic flows
    • W. JUST AND H. KANTZ, Some considerations on Poincaré maps for chaotic flows, J. Phys. A, 33 (2000), pp. 163-170.
    • (2000) J. Phys. A , vol.33 , pp. 163-170
    • JUST, W.1    KANTZ, H.2
  • 24
    • 0348091154 scopus 로고    scopus 로고
    • Computing geodesic level sets on global (un)stable manifolds of vector fields
    • B. KRAUSKOPF AND H. M. OSINGA, Computing geodesic level sets on global (un)stable manifolds of vector fields, SIAM J. Appl. Dyn. Syst., 2 (2003), pp. 546-569.
    • (2003) SIAM J. Appl. Dyn. Syst , vol.2 , pp. 546-569
    • KRAUSKOPF, B.1    OSINGA, H.M.2
  • 26
    • 54949090132 scopus 로고    scopus 로고
    • Unfolding the cusp-cusp bifurcation of planar endomorphisms
    • B. KRAUSKOPF, H. M. OSINGA, AND B. B. PECKHAM, Unfolding the cusp-cusp bifurcation of planar endomorphisms, SIAM J. Appl. Dyn. Syst., 6 (2007), pp. 403-440.
    • (2007) SIAM J. Appl. Dyn. Syst , vol.6 , pp. 403-440
    • KRAUSKOPF, B.1    OSINGA, H.M.2    PECKHAM, B.B.3
  • 28
    • 0004158141 scopus 로고
    • Cambridge University Press, Cambridge, UK
    • E. H. LOCKWOOD, A Book on Curves, Cambridge University Press, Cambridge, UK, 1961.
    • (1961) A Book on Curves
    • LOCKWOOD, E.H.1
  • 29
    • 55849112333 scopus 로고    scopus 로고
    • S. MANCINI, M. A. S. RUAS, AND M. A. TEIXEIRA, On divergent diagrams of finite codimension, Port. Math. (N.S.), 59 (2002), pp. 179-194.
    • S. MANCINI, M. A. S. RUAS, AND M. A. TEIXEIRA, , On divergent diagrams of finite codimension, Port. Math. (N.S.), 59 (2002), pp. 179-194.
  • 32
    • 55849121261 scopus 로고    scopus 로고
    • Visualization methods for vortex rings and vortex breakdown bubbles
    • The Eurographics Association, Norrköping, Sweden
    • R. PEIKERT AND F. SADLO, Visualization methods for vortex rings and vortex breakdown bubbles, in Proceedings of the Eurographics/IEEE VGTC Symposium on Visualization, The Eurographics Association, Norrköping, Sweden, 2007, pp. 211-218.
    • (2007) Proceedings of the Eurographics/IEEE VGTC Symposium on Visualization , pp. 211-218
    • PEIKERT, R.1    SADLO, F.2
  • 33
    • 55849115316 scopus 로고    scopus 로고
    • Flow topology beyond skeletons: Visualization of features in recirculating flow, in Topology-Based Methods in Visualization, Springer-Verlag, New York
    • to appear
    • R. PEIKERT AND F. SADLO, Flow topology beyond skeletons: Visualization of features in recirculating flow, in Topology-Based Methods in Visualization, Springer-Verlag, New York, to appear.
    • PEIKERT, R.1    SADLO, F.2
  • 34
    • 0000524980 scopus 로고
    • Structural stability on manifolds with boundary
    • P. B. PERCELL, Structural stability on manifolds with boundary, Topology, 12 (1973), pp. 123-144.
    • (1973) Topology , vol.12 , pp. 123-144
    • PERCELL, P.B.1
  • 37
    • 4243262725 scopus 로고    scopus 로고
    • Phase synchronization of chaotic oscillators
    • M. G. ROSENBLUM, A. S. PIKOVSKY, AND J. KURTHS, Phase synchronization of chaotic oscillators, Phys. Rev. Lett., 76 (1996), pp. 1804-1807.
    • (1996) Phys. Rev. Lett , vol.76 , pp. 1804-1807
    • ROSENBLUM, M.G.1    PIKOVSKY, A.S.2    KURTHS, J.3
  • 38
    • 0007136848 scopus 로고
    • Vector fields near the boundary of a 3-manifold
    • Dynamical Systems Valparaiso, Springer-Verlag, New York
    • J. SOTOMAYOR AND M. A. TEIXEIRA, Vector fields near the boundary of a 3-manifold, in Dynamical Systems (Valparaiso, 1986), Lecture Notes in Math. 1331, Springer-Verlag, New York, 1988, pp. 169-195.
    • (1986) Lecture Notes in Math , vol.1331 , pp. 169-195
    • SOTOMAYOR, J.1    TEIXEIRA, M.A.2
  • 40
    • 0039077177 scopus 로고
    • Generic bifurcation in manifolds with boundary
    • M. A. TEIXEIRA, Generic bifurcation in manifolds with boundary, J. Differential Equations, 25 (1977), pp. 65-89.
    • (1977) J. Differential Equations , vol.25 , pp. 65-89
    • TEIXEIRA, M.A.1
  • 41
    • 38248999679 scopus 로고
    • Generic bifurcation of sliding vector fields
    • M. A. TEIXEIRA, Generic bifurcation of sliding vector fields, J. Math. Anal. Appl., 176 (1993), pp. 436-457.
    • (1993) J. Math. Anal. Appl , vol.176 , pp. 436-457
    • TEIXEIRA, M.A.1
  • 42
    • 0001579157 scopus 로고    scopus 로고
    • Singularities of reversible vector fields
    • M. A. TEIXEIRA, Singularities of reversible vector fields, Phys. D, 100 (1997), pp. 101-118.
    • (1997) Phys. D , vol.100 , pp. 101-118
    • TEIXEIRA, M.A.1
  • 44
    • 24144493695 scopus 로고    scopus 로고
    • The dynamical complexity of optically injected semiconductor lasers
    • S. WIECZOREK, B. KRAUSKOPF, T. B. SIMPSON, AND D. LENSTRA, The dynamical complexity of optically injected semiconductor lasers, Phys. Rep., 416 (2005), pp. 1-128.
    • (2005) Phys. Rep , vol.416 , pp. 1-128
    • WIECZOREK, S.1    KRAUSKOPF, B.2    SIMPSON, T.B.3    LENSTRA, D.4
  • 45
    • 0033722842 scopus 로고    scopus 로고
    • A remark on global Poincaré section and suspension manifold
    • X.-S. YANG, A remark on global Poincaré section and suspension manifold, Chaos Solitons Fractals, 11 (2000), pp. 2157-2159.
    • (2000) Chaos Solitons Fractals , vol.11 , pp. 2157-2159
    • YANG, X.-S.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.