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Volumn 185, Issue 1, 2002, Pages 370-387

The monotonicity of period function for codimension four quadratic system Q4

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EID: 0037058005     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2002.4175     Document Type: Article
Times cited : (48)

References (53)
  • 1
    • 38249035274 scopus 로고
    • The monotonicity of the period function for planar Hamiltonian vector fields
    • C. Chicone, The monotonicity of the period function for planar Hamiltonian vector fields, J. Differential Equations 69 (1987), 310-321.
    • (1987) J. Differential Equations , vol.69 , pp. 310-321
    • Chicone, C.1
  • 2
    • 38249029275 scopus 로고
    • Geometric method for two point nonlinear boundary value problems
    • C. Chicone, Geometric method for two point nonlinear boundary value problems, J. Differential Equations 72 (1988), 360-407.
    • (1988) J. Differential Equations , vol.72 , pp. 360-407
    • Chicone, C.1
  • 3
    • 84966216689 scopus 로고
    • A quadratic system with a nonmonotonic period function
    • C. Chicone and F. Dumortier, A quadratic system with a nonmonotonic period function, Proc. Amer. Math. Soc. 102 (1988), 706-710.
    • (1988) Proc. Amer. Math. Soc , vol.102 , pp. 706-710
    • Chicone, C.1    Dumortier, F.2
  • 4
    • 0011628950 scopus 로고
    • Finiteness for critical periods of planar analytic vector fields
    • C. Chicone and F. Dumortier, Finiteness for critical periods of planar analytic vector fields, Nonlinear Anal. 20 (1993), 315-335.
    • (1993) Nonlinear Anal , vol.20 , pp. 315-335
    • Chicone, C.1    Dumortier, F.2
  • 5
    • 0000539993 scopus 로고
    • Bifurcations of critical periods for plane vector fields
    • C. Chicone and M. Jacobs, Bifurcations of critical periods for plane vector fields, Trans. Amer. Math. Soc. 312 (1989), 433-486.
    • (1989) Trans. Amer. Math. Soc , vol.312 , pp. 433-486
    • Chicone, C.1    Jacobs, M.2
  • 6
    • 44949277236 scopus 로고
    • Bifurcations of limit cycles from quadratic isochronous
    • C. Chicone and M. Jacobs, Bifurcations of limit cycles from quadratic isochronous, J. Differential Equations 91 (1991), 268-326.
    • (1991) J. Differential Equations , vol.91 , pp. 268-326
    • Chicone, C.1    Jacobs, M.2
  • 8
    • 0001792989 scopus 로고
    • On the number of critical points of period
    • S. N. Chow and J. A. Sanders, On the number of critical points of period, J. Differential Equations 64 (1986), 51-66.
    • (1986) J. Differential Equations , vol.64 , pp. 51-66
    • Chow, S.N.1    Sanders, J.A.2
  • 9
    • 0002866305 scopus 로고
    • On the monotonicity of the period function of some second order equations
    • S. N. Chow and D. Wang, On the monotonicity of the period function of some second order equations, Casopis Pest. Mat. 11 (1986), 14-25.
    • (1986) Casopis Pest. Mat , vol.11 , pp. 14-25
    • Chow, S.N.1    Wang, D.2
  • 10
    • 0036012116 scopus 로고    scopus 로고
    • The cyclicity of period annulus of degenerate quadratic Hamiltonian system with elliptic segment
    • S. N. Chow, Chengzhi Li, and Yingfei Yi, The cyclicity of period annulus of degenerate quadratic Hamiltonian system with elliptic segment, Ergodic Theory Dynamical Systems 22 (2002), 347-349.
    • (2002) Ergodic Theory Dynamical Systems , vol.22 , pp. 347-349
    • Chow, S.N.1    Li, C.2    Yi, Y.3
  • 11
    • 0039971668 scopus 로고    scopus 로고
    • Isochronous centers in planar polynomial systems
    • C. J. Christopher and J. Devlin, Isochronous centers in planar polynomial systems, SIAM J. Math. Anal. 28 (1997), 162-177.
    • (1997) SIAM J. Math. Anal , vol.28 , pp. 162-177
    • Christopher, C.J.1    Devlin, J.2
  • 12
    • 0035876989 scopus 로고    scopus 로고
    • Isochronicity into a family of time-reversible cubic vector fields
    • J. Chavarriga, I. A. García, and J. Giné, Isochronicity into a family of time-reversible cubic vector fields, Appl. Math. Comput. 121 (2001), 129-145.
    • (2001) Appl. Math. Comput , vol.121 , pp. 129-145
    • Chavarriga, J.1    García, I.A.2    Giné, J.3
  • 14
    • 0000422598 scopus 로고
    • On polynomial Hamiltonian planar vector fields
    • A. Cima, A. Gasull, and F. Manosas, On polynomial Hamiltonian planar vector fields, J. Differential Equations 106 (1993), 367-383.
    • (1993) J. Differential Equations , vol.106 , pp. 367-383
    • Cima, A.1    Gasull, A.2    Manosas, F.3
  • 15
    • 0034693569 scopus 로고    scopus 로고
    • Period function for a class of Hamiltonian systems
    • A. Cima, A. Gasull, and F. Manosas, Period function for a class of Hamiltonian systems, J. Differential Equations 168 (2000), 180-199.
    • (2000) J. Differential Equations , vol.168 , pp. 180-199
    • Cima, A.1    Gasull, A.2    Manosas, F.3
  • 16
    • 0033588749 scopus 로고    scopus 로고
    • Isochronicity for several classes of Hamiltonian system
    • A. Cima, F. Manosas, and J. Villadelprat, Isochronicity for several classes of Hamiltonian system, J. Differential Equations 157 (1999), 373-413.
    • (1999) J. Differential Equations , vol.157 , pp. 373-413
    • Cima, A.1    Manosas, F.2    Villadelprat, J.3
  • 18
    • 84972541905 scopus 로고
    • The period function of a Hamiltonian quadratic system
    • W. A. Coppel and L. Gavrilov, The period function of a Hamiltonian quadratic system, Differential Integral Equations 6 (1993), 1357-1365.
    • (1993) Differential Integral Equations , vol.6 , pp. 1357-1365
    • Coppel, W.A.1    Gavrilov, L.2
  • 19
    • 0030546995 scopus 로고    scopus 로고
    • Successive derivative of first return map, application to the study of quadratic vector fields
    • J. P. Francoise, Successive derivative of first return map, application to the study of quadratic vector fields, Ergodic Theory Dynamical Systems 1 (1996), 87-96.
    • (1996) Ergodic Theory Dynamical Systems , vol.1 , pp. 87-96
    • Francoise, J.P.1
  • 20
    • 0000047477 scopus 로고    scopus 로고
    • The first derivative of the period function of a plane vector field
    • J. P. Francoise, The first derivative of the period function of a plane vector field, Publ. Mat. 41 (1997), 127-134.
    • (1997) Publ. Mat , vol.41 , pp. 127-134
    • Francoise, J.P.1
  • 21
    • 0000415618 scopus 로고    scopus 로고
    • The period function for Hamiltonian system with homogeneous nonlinearities
    • A. Gasull, A. Guillamon, V. Manosa, and F. Manosas, The period function for Hamiltonian system with homogeneous nonlinearities, J. Differential Equations 139 (1997), 237-260.
    • (1997) J. Differential Equations , vol.139 , pp. 237-260
    • Gasull, A.1    Guillamon, A.2    Manosa, V.3    Manosas, F.4
  • 22
    • 38249004764 scopus 로고
    • Remark on the number of critical points of period
    • L. Gavrilov, Remark on the number of critical points of period, J. Differential Equations 101 (1993), 58-65.
    • (1993) J. Differential Equations , vol.101 , pp. 58-65
    • Gavrilov, L.1
  • 23
    • 0000445879 scopus 로고    scopus 로고
    • Isochronicity of plane polynomial Hamiltonian systems
    • L. Gavrilov, Isochronicity of plane polynomial Hamiltonian systems, Nonlinearity 10 (1997), 433-448.
    • (1997) Nonlinearity , vol.10 , pp. 433-448
    • Gavrilov, L.1
  • 24
    • 0035580227 scopus 로고    scopus 로고
    • The infinitesimal 16-th Hilbert problem in quadratic case
    • L. Gavrilov, The infinitesimal 16-th Hilbert problem in quadratic case, Invent. Math. 143 (2001), 449-457.
    • (2001) Invent. Math , vol.143 , pp. 449-457
    • Gavrilov, L.1
  • 25
    • 0003206189 scopus 로고    scopus 로고
    • 3 singularity and perturbation of the spherical pendulum
    • 3 singularity and perturbation of the spherical pendulum, Compositio Math. 123 (2000), 167-184.
    • (2000) Compositio Math , vol.123 , pp. 167-184
    • Gavrilov, L.1    Vivolo, O.2
  • 26
    • 0000857278 scopus 로고
    • A remark on the period of the periodic solution in the Lotka-Volterra systems
    • Sze-Bi Hsu, A remark on the period of the periodic solution in the Lotka-Volterra systems, J. Math. Anal. Appl. 95 (1983), 428-436.
    • (1983) J. Math. Anal. Appl , vol.95 , pp. 428-436
    • Hsu, S.-B.1
  • 27
    • 21944453138 scopus 로고    scopus 로고
    • Inhomogeneous Fuchs equations and the limit cycles in a class of near-integrable quadratic systems
    • I. D. Iliev, Inhomogeneous Fuchs equations and the limit cycles in a class of near-integrable quadratic systems, Proc. Roy. Soc. Edinburgh, 127A (1997), 1207-1217.
    • (1997) Proc. Roy. Soc. Edinburgh , vol.127 A , pp. 1207-1217
    • Iliev, I.D.1
  • 28
    • 0032020006 scopus 로고    scopus 로고
    • Perturbations of quadratic centers
    • I. D. Iliev, Perturbations of quadratic centers, Bull. Sci. Math. 122 (1998), 107-161.
    • (1998) Bull. Sci. Math , vol.122 , pp. 107-161
    • Iliev, I.D.1
  • 29
    • 0002487294 scopus 로고
    • Behaviour of the period of solutions of certain plane autonomous systems near centers
    • W. S. Loud, Behaviour of the period of solutions of certain plane autonomous systems near centers, Contrib. Differential Equations 3 (1964), 21-36.
    • (1964) Contrib. Differential Equations , vol.3 , pp. 21-36
    • Loud, W.S.1
  • 30
    • 0001228987 scopus 로고    scopus 로고
    • Darboux linearization and isochronous centers with rational first integral
    • P. Mardesic, L. Moser-Jauslin, and C. Rousseau, Darboux linearization and isochronous centers with rational first integral, J. Differential Equations 134 (1997), 216-268.
    • (1997) J. Differential Equations , vol.134 , pp. 216-268
    • Mardesic, P.1    Moser-Jauslin, L.2    Rousseau, C.3
  • 32
    • 21844508050 scopus 로고
    • Simple exponential estimate for the number of real zeros of complete Abelian integrals
    • D. Novikov and S. Yakovenko, Simple exponential estimate for the number of real zeros of complete Abelian integrals, Ann. Inst. Fourier 45 (1995), 897-927.
    • (1995) Ann. Inst. Fourier , vol.45 , pp. 897-927
    • Novikov, D.1    Yakovenko, S.2
  • 33
    • 0001799622 scopus 로고
    • Number of zeros of complete elliptic integrals
    • G. S. Petrov, Number of zeros of complete elliptic integrals, Func. Anal. Appl. 18 (1984), 73-74.
    • (1984) Func. Anal. Appl , vol.18 , pp. 73-74
    • Petrov, G.S.1
  • 34
    • 0001639716 scopus 로고
    • A new method of investigating the isochronicity of a system of two differential equations
    • I. Pleshkan, A new method of investigating the isochronicity of a system of two differential equations, Differential Equations 5 (1969), 796-802.
    • (1969) Differential Equations , vol.5 , pp. 796-802
    • Pleshkan, I.1
  • 35
    • 0001417925 scopus 로고
    • Thermodynamics, real and complex periods of the Volterra model
    • F. Rothe, Thermodynamics, real and complex periods of the Volterra model, Z. Angew. Math. Phys. 36 (1985), 395-421.
    • (1985) Z. Angew. Math. Phys , vol.36 , pp. 395-421
    • Rothe, F.1
  • 36
    • 84920547916 scopus 로고
    • The periods of the Volterra-Lotka system
    • F. Rothe, The periods of the Volterra-Lotka system, J. Reine Angew. Math. 355 (1985), 129-138.
    • (1985) J. Reine Angew. Math , vol.355 , pp. 129-138
    • Rothe, F.1
  • 38
    • 0031508104 scopus 로고    scopus 로고
    • Local bifurcation of critical periods in the reduced Kukles system
    • C. Rousseau and B. Toni, Local bifurcation of critical periods in the reduced Kukles system, Can. J. Math. 49 (1997), 338-358.
    • (1997) Can. J. Math , vol.49 , pp. 338-358
    • Rousseau, C.1    Toni, B.2
  • 39
    • 44949281273 scopus 로고
    • Zeros of complete elliptic integrals for 1:2 resonance
    • C. Rousseau and H. Zoladek, Zeros of complete elliptic integrals for 1:2 resonance, J. Differential Equations 94 (1991), 42-54.
    • (1991) J. Differential Equations , vol.94 , pp. 42-54
    • Rousseau, C.1    Zoladek, H.2
  • 40
    • 0032329942 scopus 로고    scopus 로고
    • A connection between isochronous Hamiltonian centers and the Jacobian conjecture
    • M. Sabatini, A connection between isochronous Hamiltonian centers and the Jacobian conjecture, Nonlinear Appl. 34 (1998), 829-838.
    • (1998) Nonlinear Appl , vol.34 , pp. 829-838
    • Sabatini, M.1
  • 41
    • 0033095591 scopus 로고    scopus 로고
    • On the period function of Liénard system
    • M. Sabatini, On the period function of Liénard system, J. Differential Equations 152 (1999), 467-487.
    • (1999) J. Differential Equations , vol.152 , pp. 467-487
    • Sabatini, M.1
  • 42
    • 3042708227 scopus 로고
    • Global behaviour of solution branches for some Neumann problems depending on one or several parameters
    • R. Schaaf, Global behaviour of solution branches for some Neumann problems depending on one or several parameters, J. Reine Angew. Math. 346 (1984), 1-31.
    • (1984) J. Reine Angew. Math , vol.346 , pp. 1-31
    • Schaaf, R.1
  • 43
    • 0002499881 scopus 로고
    • A class of Hamiltonian system with increasing periods
    • R. Schaaf, A class of Hamiltonian system with increasing periods, J. Reine Angew. Math. 363 (1985), 96-109.
    • (1985) J. Reine Angew. Math , vol.363 , pp. 96-109
    • Schaaf, R.1
  • 44
    • 0000353375 scopus 로고
    • Regularity properties of the period function near a center of planar vector fields
    • M. Villarini, Regularity properties of the period function near a center of planar vector fields, Nonlinear Anal. Theory Methods Appl. 8 (1992), 787-803.
    • (1992) Nonlinear Anal. Theory Methods Appl , vol.8 , pp. 787-803
    • Villarini, M.1
  • 45
    • 0011572650 scopus 로고
    • The period in the Volterra-Lotka predator prey model
    • J. Waldvogel, The period in the Volterra-Lotka predator prey model, SIAM J. Number Anal. 20 (1983), 1264-1272.
    • (1983) SIAM J. Number Anal , vol.20 , pp. 1264-1272
    • Waldvogel, J.1
  • 46
    • 0022661610 scopus 로고
    • The period in the Lotka-Volterra system is monotonic
    • J. Waldvogel, The period in the Lotka-Volterra system is monotonic, J. Math. Anal. Appl. 114 (1986), 178-184.
    • (1986) J. Math. Anal. Appl , vol.114 , pp. 178-184
    • Waldvogel, J.1
  • 47
    • 0002061737 scopus 로고
    • On the existence of 2π-periodic solutions of the differential equation ẍ + g(x) = p(t)
    • [In Chinese]
    • D. Wang, On the existence of 2π-periodic solutions of the differential equation ẍ + g(x) = p(t), Chinese Ann. Math. Ser. A 5 (1984), 61-72. [In Chinese]
    • (1984) Chinese Ann. Math. Ser. A , vol.5 , pp. 61-72
    • Wang, D.1
  • 48
    • 38249037671 scopus 로고
    • 2(x - α)(x - 1) = 0 (0 ≤ α < 1)
    • 2(x - α)(x - 1) = 0 (0 ≤ α < 1), Nonlinear Anal. 11 (1987), 1029-1050.
    • (1987) Nonlinear Anal , vol.11 , pp. 1029-1050
    • Wang, D.1
  • 49
    • 0000813963 scopus 로고
    • Quadratic systems with centers and their perturbations
    • H. Zoladek, Quadratic systems with centers and their perturbations, J. Differential Equations 109 (1994), 223-273.
    • (1994) J. Differential Equations , vol.109 , pp. 223-273
    • Zoladek, H.1
  • 50
    • 0034688727 scopus 로고    scopus 로고
    • The cyclicity of the period annulus of the quadratic Hamiltonian systems with non-Morsean point
    • Y. Zhao, Z. Liang, and G. Lu, The cyclicity of the period annulus of the quadratic Hamiltonian systems with non-Morsean point, J. Differential Equations 162 (2000), 199-223.
    • (2000) J. Differential Equations , vol.162 , pp. 199-223
    • Zhao, Y.1    Liang, Z.2    Lu, G.3
  • 51
    • 0035256188 scopus 로고    scopus 로고
    • Perturbations of the non-generic quadratic Hamiltonian vector fields with hyperbolic segment
    • Y. Zhao and S. Zhu, Perturbations of the non-generic quadratic Hamiltonian vector fields with hyperbolic segment, Bull. Sci. Math. 125 (2001), 109-138.
    • (2001) Bull. Sci. Math , vol.125 , pp. 109-138
    • Zhao, Y.1    Zhu, S.2
  • 52
    • 0000564377 scopus 로고    scopus 로고
    • Abelian integrals for cubic vector fields
    • Y. Zhao and Z. Zhang, Abelian integrals for cubic vector fields, Ann. Mat. Pura Appl. CLXXVI (1999), 251-272.
    • (1999) Ann. Mat. Pura Appl , vol.176 , pp. 251-272
    • Zhao, Y.1    Zhang, Z.2
  • 53
    • 0033542307 scopus 로고    scopus 로고
    • Linear estimate of the number of zeros of Abelian integrals for a kind of quartic Hamiltonians
    • Y. Zhao and Z. Zhang, Linear estimate of the number of zeros of Abelian integrals for a kind of quartic Hamiltonians, J. Differential Equations 155 (1999), 73-88.
    • (1999) J. Differential Equations , vol.155 , pp. 73-88
    • Zhao, Y.1    Zhang, Z.2


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