메뉴 건너뛰기




Volumn 16, Issue 1, 2011, Pages 154-184

Quasi-periodic bifurcations of invariant circles in low-dimensional dissipative dynamical systems

Author keywords

bifurcations; invariant tori; KAM theory; resonances

Indexed keywords


EID: 79952016042     PISSN: 15603547     EISSN: 14684845     Source Type: Journal    
DOI: 10.1134/S1560354711010060     Document Type: Article
Times cited : (92)

References (75)
  • 1
    • 0242275980 scopus 로고    scopus 로고
    • Resonance Tongues and Instability Pockets in the Quasi-periodic Hill-Schrödinger Equation
    • Broer, H. W., Puig, J., and Simó, C., Resonance Tongues and Instability Pockets in the Quasi-periodic Hill-Schrödinger Equation. Comm. Math. l Phys., 2003, vol. 241, pp. 467-503.
    • (2003) Comm. Math.L Phys. , vol.241 , pp. 467-503
    • Broer, H.W.1    Puig, J.2    Simó, C.3
  • 2
    • 27144516452 scopus 로고    scopus 로고
    • Hill's Equation with Quasi-periodic Forcing: Resonance Tongues, Instability Pockets and Global Phenomena
    • Broer, H. W and Simó, C., Hill's Equation with Quasi-periodic Forcing: Resonance Tongues, Instability Pockets and Global Phenomena, Boletim Sociedade Brasileira Matemática, 1998, vol. 29, pp. 253-293.
    • (1998) Boletim Sociedade Brasileira Matemática , vol.29 , pp. 253-293
    • Broer, H.W.1    Simó, C.2
  • 4
    • 53149138221 scopus 로고    scopus 로고
    • Integrable and Non-Integrable Deformations of the Skew Hopf Bifurcation
    • Broer, H. W., Takens, F., and Wagener, F. O. O., Integrable and Non-Integrable Deformations of the Skew Hopf Bifurcation, Regul. Chaotic Dyn., 1999, vol. 4, no. 2, pp. 16-43.
    • (1999) Regul. Chaotic Dyn. , vol.4 , Issue.2 , pp. 16-43
    • Broer, H.W.1    Takens, F.2    Wagener, F.O.O.3
  • 5
    • 0034409608 scopus 로고    scopus 로고
    • Quasi-Periodic Stability of Subfamilies of an Unfolded Skew Hopf Bifurcation
    • Broer, H. W. and Wagener, F. O. O., Quasi-Periodic Stability of Subfamilies of an Unfolded Skew Hopf Bifurcation, Arch. Ration. Mech. Anal., 2000, vol. 152, pp. 283-326.
    • (2000) Arch. Ration. Mech. Anal. , vol.152 , pp. 283-326
    • Broer, H.W.1    Wagener, F.O.O.2
  • 8
    • 0039621597 scopus 로고    scopus 로고
    • Resonances in Skew and Reducible Quasi-Periodic Hopf Bifurcations
    • Takens, F. and Wagener, F. O. O., Resonances in Skew and Reducible Quasi-Periodic Hopf Bifurcations, Nonlinearity, 2000, vol. 13, no. 2, pp. 377-396.
    • (2000) Nonlinearity , vol.13 , Issue.2 , pp. 377-396
    • Takens, F.1    Wagener, F.O.O.2
  • 9
    • 67650718095 scopus 로고    scopus 로고
    • Normal Forms in Perturbation Theory
    • R. Meyers (Ed.), New York: Springer
    • Broer, H. W., Normal Forms in Perturbation Theory, Encyclopœia of Complexity & System Science, R. Meyers (Ed.) New York: Springer, 2009, pp. 6310-6329.
    • (2009) Encyclopœia of Complexity & System Science , pp. 6310-6329
    • Broer, H.W.1
  • 10
    • 0001811172 scopus 로고
    • Towards a Quasi-Periodic Bifurcation Theory
    • Braaksma, B. L. J., Broer, H. W., and Huitema, G. B., Towards a Quasi-Periodic Bifurcation Theory, Mem. Amer. Math. Soc., 1990, vol. 83, no. 421, pp. 83-175.
    • (1990) Mem. Amer. Math. Soc. , vol.83 , Issue.421 , pp. 83-175
    • Braaksma, B.L.J.1    Broer, H.W.2    Huitema, G.B.3
  • 11
    • 33750612100 scopus 로고    scopus 로고
    • Normal Linear Stability of Quasi-Periodic Tori
    • Broer, H. W., Hoo, J., and Naudot, V., Normal Linear Stability of Quasi-Periodic Tori, J. Differential Equations, 2007, vol. 232, no. 2, pp. 355-418.
    • (2007) J. Differential Equations , vol.232 , Issue.2 , pp. 355-418
    • Broer, H.W.1    Hoo, J.2    Naudot, V.3
  • 12
    • 0001874618 scopus 로고
    • Unfoldings of Quasi-Periodic Tori
    • Broer, H. W., Huitema, G. B., and Takens, F., Unfoldings of Quasi-Periodic Tori, Mem. Amer. Math. Soc., 1990, vol. 83, no. 421, pp. 1-82.
    • (1990) Mem. Amer. Math. Soc. , vol.83 , Issue.421 , pp. 1-82
    • Broer, H.W.1    Huitema, G.B.2    Takens, F.3
  • 14
    • 0003706768 scopus 로고
    • Lecture Notes in Math, Berlin-New York: Springer
    • Hirsch, M. W., Pugh, C. C., and Shub, M., Invariant Manifolds, Lecture Notes in Math., vol. 583, Berlin-New York: Springer, 1977.
    • (1977) Invariant Manifolds , vol.583
    • Hirsch, M.W.1    Pugh, C.C.2    Shub, M.3
  • 17
    • 24144464514 scopus 로고    scopus 로고
    • On the Quasi-Periodic d-fold Degenerate Bifurcation
    • Wagener, F. O. O., On the Quasi-Periodic d-fold Degenerate Bifurcation, J. Differential Equations, 2005, vol. 216, no. 2, pp. 261-281.
    • (2005) J. Differential Equations , vol.216 , Issue.2 , pp. 261-281
    • Wagener, F.O.O.1
  • 18
    • 79952018443 scopus 로고    scopus 로고
    • A Parametrised Version of Moser's Modifying Terms Theorem
    • Wagener, F. O. O., A Parametrised Version of Moser's Modifying Terms Theorem, Discrete Contin. Dyn. Syst. Ser. S, 2010, vol. 3, no. 4, pp. 719-768.
    • (2010) Discrete Contin. Dyn. Syst. Ser. S , vol.3 , Issue.4 , pp. 719-768
    • Wagener, F.O.O.1
  • 19
    • 51649147118 scopus 로고
    • Bifurcations de points fixes elliptiques: I. Courbes invariantes
    • Chenciner, A., Bifurcations de points fixes elliptiques: I. Courbes invariantes, Inst. Hautes Études Sci. Publ. Math., 1985, vol. 61, pp. 67-127.
    • (1985) Inst. Hautes Études Sci. Publ. Math. , vol.61 , pp. 67-127
    • Chenciner, A.1
  • 20
    • 0013369791 scopus 로고
    • Bifurcations de points fixes elliptiques: II. Orbites périodiques et ensembles de Cantor invariants
    • Chenciner, A., Bifurcations de points fixes elliptiques: II. Orbites périodiques et ensembles de Cantor invariants, Invent. Math., 1985, vol. 80, no. 1, pp. 81-106.
    • (1985) Invent. Math. , vol.80 , Issue.1 , pp. 81-106
    • Chenciner, A.1
  • 21
    • 51649147531 scopus 로고
    • Bifurcations de points fixes elliptiques: III. Orbites périodiques de "petites" périodes et élimination résonante des couples de courbes invariantes
    • Chenciner, A., Bifurcations de points fixes elliptiques: III. Orbites périodiques de "petites" périodes et élimination résonante des couples de courbes invariantes, Inst. Hautes Études Sci. Publ. Math., 1987, vol. 66, pp. 5-91.
    • (1987) Inst. Hautes Études Sci. Publ. Math. , vol.66 , pp. 5-91
    • Chenciner, A.1
  • 22
    • 0010138127 scopus 로고    scopus 로고
    • The Quasi-Periodic Centre-Saddle Bifurcation
    • Hanßmann, H., The Quasi-Periodic Centre-Saddle Bifurcation, J. Differential Equations, 1998, vol. 142, pp. 305-370.
    • (1998) J. Differential Equations , vol.142 , pp. 305-370
    • Hanßmann, H.1
  • 23
    • 21244442290 scopus 로고    scopus 로고
    • Bifurcations of Normally Parabolic Tori in Hamiltonian Systems
    • Broer, H. W., Hanßmann, H., and You, J., Bifurcations of Normally Parabolic Tori in Hamiltonian Systems, Nonlinearity, 2005, vol. 18, no. 4, pp. 1735-1769.
    • (2005) Nonlinearity , vol.18 , Issue.4 , pp. 1735-1769
    • Broer, H.W.1    Hanßmann, H.2    You, J.3
  • 24
    • 32044436274 scopus 로고    scopus 로고
    • Umbilical Torus Bifurcations in Hamiltonian Systems
    • Broer, H. W., Hanßmann, H., and You, J., Umbilical Torus Bifurcations in Hamiltonian Systems, J. Differential Equations, 2006, vol. 222, no. 1, pp. 233-262.
    • (2006) J. Differential Equations , vol.222 , Issue.1 , pp. 233-262
    • Broer, H.W.1    Hanßmann, H.2    You, J.3
  • 27
    • 33646002283 scopus 로고    scopus 로고
    • Survey on Dissipative kam Theory Including Quasi-Periodic Bifurcation Theory: Based on Lectures by Henk Broer
    • London Math. Soc. Lecture Note Ser, J. Montaldi and T. Ratiu (Eds.), Cambridge: Cambridge Univ. Press
    • Ciocci, M. C., Litvak-Hinenzon, A., and Broer, H. W., Survey on Dissipative kam Theory Including Quasi-Periodic Bifurcation Theory: Based on Lectures by Henk Broer, Geometric Mechanics and Symmetry: The Peyresq Lectures, J. Montaldi and T. Ratiu (Eds.), London Math. Soc. Lecture Note Ser., vol. 306, Cambridge: Cambridge Univ. Press, 2005, pp. 303-355.
    • (2005) Geometric Mechanics and Symmetry: The Peyresq Lectures , vol.306 , pp. 303-355
    • Ciocci, M.C.1    Litvak-Hinenzon, A.2    Broer, H.W.3
  • 28
    • 21344488160 scopus 로고
    • Mixed Spectrum and Rotational Symmetry
    • Broer, H. W. and Takens, F., Mixed Spectrum and Rotational Symmetry, Arch. Ration. Mech. Anal., 1993, vol. 124, pp. 13-42.
    • (1993) Arch. Ration. Mech. Anal. , vol.124 , pp. 13-42
    • Broer, H.W.1    Takens, F.2
  • 31
    • 58149498523 scopus 로고    scopus 로고
    • Quasi-Periodic Stability of Normally Resonant Tori
    • Broer, H. W., Ciocci, M. C., Hanßann, H., and Vanderbauwhede, A., Quasi-Periodic Stability of Normally Resonant Tori, Phys. D, 2009, vol. 238, no. 3, pp. 309-318.
    • (2009) Phys. D , vol.238 , Issue.3 , pp. 309-318
    • Broer, H.W.1    Ciocci, M.C.2    Hanßann, H.3    Vanderbauwhede, A.4
  • 32
    • 33947682204 scopus 로고    scopus 로고
    • The Quasi-Periodic Hamiltonian Hopf Bifurcation
    • Broer, H. W., Hanßann, H., and Hoo, J., The Quasi-Periodic Hamiltonian Hopf Bifurcation, Nonlinearity, 2007, vol. 20, no. 2, pp. 417-460.
    • (2007) Nonlinearity , vol.20 , Issue.2 , pp. 417-460
    • Broer, H.W.1    Hanßann, H.2    Hoo, J.3
  • 34
    • 0006963160 scopus 로고    scopus 로고
    • Towards Global Models Near Homoclinic Tangencies of Dissipative Diffeomorphisms
    • Broer, H. W., Simó, C., Tatjer, J. C., Towards Global Models Near Homoclinic Tangencies of Dissipative Diffeomorphisms, Nonlinearity, 1998, vol. 11, no. 3, pp. 667-770.
    • (1998) Nonlinearity , vol.11 , Issue.3 , pp. 667-770
    • Broer, H.W.1    Simó, C.2    Tatjer, J.C.3
  • 35
    • 0142137606 scopus 로고    scopus 로고
    • Normal-Internal Resonances in Quasi-Periodically Forced Oscillators: A Conservative Approach
    • Broer, H. W., Hanßann, H., Jorba, À., Villanueva, J., and Wagener, F. O. O., Normal-Internal Resonances in Quasi-Periodically Forced Oscillators: A Conservative Approach, Nonlinearity, 2003, vol. 16, no. 5, pp. 1751-1791.
    • (2003) Nonlinearity , vol.16 , Issue.5 , pp. 1751-1791
    • Broer, H.W.1    Hanßann, H.2    Jorba3    Villanueva, J.4    Wagener, F.O.O.5
  • 36
    • 79952024665 scopus 로고    scopus 로고
    • Dynamics and Geometry Near Resonant Bifurcations
    • Broer, H. W., Holtman, S. J., Vegter, G., and Vitolo, R., Dynamics and Geometry Near Resonant Bifurcations, Regul. Chaotic Dyn., 2011, vol. 16, nos. 1-2, pp. 39-50.
    • (2011) Regul. Chaotic Dyn. , vol.16 , Issue.1-2 , pp. 39-50
    • Broer, H.W.1    Holtman, S.J.2    Vegter, G.3    Vitolo, R.4
  • 37
    • 44949236072 scopus 로고    scopus 로고
    • Generic Hopf-Neǐmark-Sacker Bifurcations in Feed Forward Systems
    • Broer, H. W. and Vegter, G., Generic Hopf-Neǐmark-Sacker Bifurcations in Feed Forward Systems, Nonlinearity, 2008, vol. 21, pp. 1547-1578.
    • (2008) Nonlinearity , vol.21 , pp. 1547-1578
    • Broer, H.W.1    Vegter, G.2
  • 39
    • 0040845842 scopus 로고    scopus 로고
    • On the Vertical Families of Two-Dimensional Tori Near the Triangular Points of the Bicircular Problem
    • Castellà, E. and Jorba, À., On the Vertical Families of Two-Dimensional Tori Near the Triangular Points of the Bicircular Problem, Celestial Mech. Dynam. Astronom., 2000, vol. 76, no. 1, pp. 35-54.
    • (2000) Celestial Mech. Dynam. Astronom. , vol.76 , Issue.1 , pp. 35-54
    • Castellà, E.1    Jorba2
  • 40
    • 0040483472 scopus 로고    scopus 로고
    • Numerical Computation of the Normal Behaviour of Invariant Curves of n-Dimensional Maps
    • Jorba, À., Numerical Computation of the Normal Behaviour of Invariant Curves of n-Dimensional Maps, Nonlinearity, 2001 vol. 14, no. 5, pp. 943-976.
    • (2001) Nonlinearity , vol.14 , Issue.5 , pp. 943-976
    • Jorba1
  • 41
    • 77957816363 scopus 로고    scopus 로고
    • A Collocation Method for the Numerical Fourier Analysis of Quasi-Periodic Functions: I.Numerical Tests and Examples
    • Gómez, G., Mondelo, J.-M., and Simó, C., A Collocation Method for the Numerical Fourier Analysis of Quasi-Periodic Functions: I. Numerical Tests and Examples, Discrete Contin. Dyn. Syst. Ser. B, 2010, vol. 14, no. 1, pp. 41-74.
    • (2010) Discrete Contin. Dyn. Syst. Ser. B , vol.14 , Issue.1 , pp. 41-74
    • Gómez, G.1    Mondelo, J.-M.2    Simó, C.3
  • 42
    • 77957761095 scopus 로고    scopus 로고
    • A Collocation Method for the Numerical Fourier Analysis of Quasi-Periodic Functions: II.Analytical Error Estimates
    • Gómez, G., Mondelo, J.-M., and Simó, C., A Collocation Method for the Numerical Fourier Analysis of Quasi-Periodic Functions: II. Analytical Error Estimates, Discrete Contin. Dyn. Syst. Ser. B, 2010, vol. 14, no. 1, pp. 75-109.
    • (2010) Discrete Contin. Dyn. Syst. Ser. B , vol.14 , Issue.1 , pp. 75-109
    • Gómez, G.1    Mondelo, J.-M.2    Simó, C.3
  • 44
    • 33746548476 scopus 로고    scopus 로고
    • A Parameterization Method for the Computation of Invariant Tori and Their Whiskers in Quasi-Periodic Maps: Rigorous Results
    • Haro, À. and de la Llave, R., A Parameterization Method for the Computation of Invariant Tori and Their Whiskers in Quasi-Periodic Maps: Rigorous Results, J. Differential Equations, 2006, vol. 228, no. 2, pp. 530-579.
    • (2006) J. Differential Equations , vol.228 , Issue.2 , pp. 530-579
    • Haro1    de la Llave, R.2
  • 45
    • 33750532700 scopus 로고    scopus 로고
    • A Parameterization Method for the Computation of Invariant Tori and Their Whiskers in Quasi-Periodic Maps: Numerical Algorithms
    • Haro, À. and de la Llave, R., A Parameterization Method for the Computation of Invariant Tori and Their Whiskers in Quasi-Periodic Maps: Numerical Algorithms, Discrete Contin. Dyn. Syst. Ser. B, 2006, vol. 6, no. 6, pp. 1261-1300.
    • (2006) Discrete Contin. Dyn. Syst. Ser. B , vol.6 , Issue.6 , pp. 1261-1300
    • Haro1    de la Llave, R.2
  • 46
    • 45049087511 scopus 로고    scopus 로고
    • A ParameterizationMethod for the Computation of Invariant Tori and Their Whiskers in Quasi-Periodic Maps: Explorations and Mechanisms for the Breakdown of Hyperbolicity
    • Haro, À. and de la Llave, R., A ParameterizationMethod for the Computation of Invariant Tori and Their Whiskers in Quasi-Periodic Maps: Explorations and Mechanisms for the Breakdown of Hyperbolicity, SIAM J. Appl. Dyn. Syst., 2007, vol. 6, no. 1, pp. 142-207.
    • (2007) SIAM J. Appl. Dyn. Syst. , vol.6 , Issue.1 , pp. 142-207
    • Haro1    de la Llave, R.2
  • 47
    • 33644886647 scopus 로고    scopus 로고
    • Continuation of Quasi-Periodic Invariant Tori
    • Schilder, F., Osinga, H. M., and Vogt, W., Continuation of Quasi-Periodic Invariant Tori, SIAM J. Appl. Dyn. Syst., 2005, vol. 4, no. 3, pp. 459-488.
    • (2005) SIAM J. Appl. Dyn. Syst. , vol.4 , Issue.3 , pp. 459-488
    • Schilder, F.1    Osinga, H.M.2    Vogt, W.3
  • 48
    • 33750510588 scopus 로고    scopus 로고
    • Effective Computations in Hamiltonian Dynamics
    • SMF Journ. Annu, A. Chenciner, C. Simó (Eds.), Paris: Soc. Math. France
    • Simó, C., Effective Computations in Hamiltonian Dynamics, Mécanique celeste, A. Chenciner and C. Simó (Eds.), SMF Journ. Annu., vol. 1996, Paris: Soc. Math. France, 1996.
    • (1996) Mécanique Celeste , vol.1996
    • Simó, C.1
  • 49
    • 0009318412 scopus 로고    scopus 로고
    • Effective Computations in Celestial Mechanics and Astrodynamics
    • CISM Courses and Lectures, V. V. Rumyantsev and A. V. Karapetyan (Eds.), Vienna: Springer
    • C. Simó, Effective Computations in Celestial Mechanics and Astrodynamics. In Modern Methods of Analytical Mechanics and their Applications (Udine, 1997), V. V. Rumyantsev and A. V. Karapetyan (Eds.), CISM Courses and Lectures, vol. 387, Vienna: Springer, 1998, pp. 55-102. Available also at http://www. maia. ub. es/dsg/1997/.
    • (1998) Modern Methods of Analytical Mechanics and Their Applications (Udine, 1997) , vol.387 , pp. 55-102
    • Simó, C.1
  • 51
    • 0042384678 scopus 로고    scopus 로고
    • Bifurcations and Strange Attractors in the Lorenz-84 Climate Model with Seasonal Forcing
    • Broer, H. W., Simó, C., and Vitolo, R., Bifurcations and Strange Attractors in the Lorenz-84 Climate Model with Seasonal Forcing, Nonlinearity, 2002, vol. 15, no. 4, pp. 1205-1267.
    • (2002) Nonlinearity , vol.15 , Issue.4 , pp. 1205-1267
    • Broer, H.W.1    Simó, C.2    Vitolo, R.3
  • 52
    • 78149354879 scopus 로고    scopus 로고
    • Routes to Chaos in the Hopf-Saddle-Node Bifurcation for Fixed Points of 3D-diffeomorphisms
    • Vitolo, R., Broer, H. W., and Simó, C., Routes to Chaos in the Hopf-Saddle-Node Bifurcation for Fixed Points of 3D-diffeomorphisms, Nonlinearity, 2010, vol. 23, no. 8, pp. 1919-1947.
    • (2010) Nonlinearity , vol.23 , Issue.8 , pp. 1919-1947
    • Vitolo, R.1    Broer, H.W.2    Simó, C.3
  • 53
    • 45049085469 scopus 로고    scopus 로고
    • The Hopf-Saddle-Node Bifurcation for Fixed Points of 3D diffeomorphisms: Analysis of a resonance "bubble"
    • Broer, H. W., Simó, C., and Vitolo, R., The Hopf-Saddle-Node Bifurcation for Fixed Points of 3D diffeomorphisms: Analysis of a resonance "bubble", Phys. D, 2008, vol. 237, no. 13, pp. 1773-1799.
    • (2008) Phys. D , vol.237 , Issue.13 , pp. 1773-1799
    • Broer, H.W.1    Simó, C.2    Vitolo, R.3
  • 54
    • 56349155062 scopus 로고    scopus 로고
    • The Hopf-Saddle-Node Bifurcation for Fixed Points of 3Ddiffeomorphisms: The Arnol'd Resonance Web
    • Broer, H. W., Simó, C., and Vitolo, R., The Hopf-Saddle-Node Bifurcation for Fixed Points of 3Ddiffeomorphisms: The Arnol'd Resonance Web, Bull. Belg. Math. Soc. Simon Stevin, 2008, vol. 15, no. 5, pp. 769-787.
    • (2008) Bull. Belg. Math. Soc. Simon Stevin , vol.15 , Issue.5 , pp. 769-787
    • Broer, H.W.1    Simó, C.2    Vitolo, R.3
  • 55
    • 73149109691 scopus 로고    scopus 로고
    • A Mechanism for the Fractalization of Invariant Curves in Quasi-Periodically Forced 1 - D maps
    • Jorba, À. and Tatjer, J. C., A Mechanism for the Fractalization of Invariant Curves in Quasi-Periodically Forced 1 - D maps, Discrete Contin. Dyn. Syst. Ser. B, 2008, vol. 10, nos. 2-3, pp. 537-567.
    • (2008) Discrete Contin. Dyn. Syst. Ser. B , vol.10 , Issue.2-3 , pp. 537-567
    • Jorba1    Tatjer, J.C.2
  • 56
    • 0347550175 scopus 로고
    • Quasi-Genericity of Bifurcations to High-Dimensional Invariant Tori for Maps
    • Iooss, G. and Los, J. E., Quasi-Genericity of Bifurcations to High-Dimensional Invariant Tori for Maps, Comm. Math. Phys., 1988, vol. 119, no. 3, pp. 453-500.
    • (1988) Comm. Math. Phys. , vol.119 , Issue.3 , pp. 453-500
    • Iooss, G.1    Los, J.E.2
  • 57
    • 0007142221 scopus 로고
    • Bifurcations de tores invariants
    • Chenciner, A. and Iooss, G., Bifurcations de tores invariants, Arch. Ration. Mech. Anal., 1979, vol. 69, no. 2, pp. 109-198.
    • (1979) Arch. Ration. Mech. Anal. , vol.69 , Issue.2 , pp. 109-198
    • Chenciner, A.1    Iooss, G.2
  • 58
    • 77957172363 scopus 로고
    • Dédoublement de courbes invariantes sur le cylindre: Petit diviseurs
    • Los, J., Dédoublement de courbes invariantes sur le cylindre: Petit diviseurs, Ann. Inst. H. Poincaré Anal. Non Linéaire, 1988, vol. 5, pp. 37-95.
    • (1988) Ann. Inst. H.Poincaré Anal. Non Linéaire , vol.5 , pp. 37-95
    • Los, J.1
  • 59
    • 0003053628 scopus 로고
    • On the Analytical and Numerical Computation of Invariant Manifolds
    • D. Benest, C. Froeschlé (Eds.), Paris: Frontières
    • Simó, C., On the Analytical and Numerical Computation of Invariant Manifolds, Modern Methods in Celestial Mechanics, D. Benest and C. Froeschlé (Eds.), Paris: Frontières, 1990, pp. 285-330. Available also at http://www. maia. ub. es/dsg/2004/.
    • (1990) Modern Methods in Celestial Mechanics , pp. 285-330
    • Simó, C.1
  • 62
    • 0347550173 scopus 로고
    • 3 and Doubling Bifurcation
    • 3 and Doubling Bifurcation, Nonlinearity, 1989, vol. 2, no. 1, pp. 149-174.
    • (1989) Nonlinearity , vol.2 , Issue.1 , pp. 149-174
    • Los, J.1
  • 63
    • 25144520508 scopus 로고    scopus 로고
    • The Quasi-Periodic Doubling Cascade in the Transition to Weak Turbulence
    • van Veen, L., The Quasi-Periodic Doubling Cascade in the Transition to Weak Turbulence, Phys. D, 2005, vol. 210, nos. 3-4, pp. 249-261.
    • (2005) Phys. D , vol.210 , Issue.3-4 , pp. 249-261
    • van Veen, L.1
  • 64
    • 79952036293 scopus 로고    scopus 로고
    • Resonance Tongues and Spectral Gaps in Quasi-Periodic Schrödinger Operators with One or More Frequencies: A Numerical Exploration
    • (to appear)
    • Puig, J. and Simó, C., Resonance Tongues and Spectral Gaps in Quasi-Periodic Schrödinger Operators with One or More Frequencies: A Numerical Exploration, J. Dynam. Differential Equations, 2011 (to appear).
    • (2011) J. Dynam. Differential Equations
    • Puig, J.1    Simó, C.2
  • 65
    • 79952026919 scopus 로고    scopus 로고
    • Resonance Tongues in the Quasi-Periodic Hill-Schrödinger Equation with Three Frequencies
    • Puig, J. and Simó, C., Resonance Tongues in the Quasi-Periodic Hill-Schrödinger Equation with Three Frequencies, Regul. Chaotic Dyn., 2011, vol. 16, nos. 1-2, pp. 61-78.
    • (2011) Regul. Chaotic Dyn. , vol.16 , Issue.1-2 , pp. 61-78
    • Puig, J.1    Simó, C.2
  • 66
    • 44949274027 scopus 로고
    • Three Coupled Oscillators: Mode-locking, Global Bifurcations and Toroidal Chaos
    • Baesens, C., Guckenheimer, J., Kim, S., and MacKay, R. S., Three Coupled Oscillators: Mode-locking, Global Bifurcations and Toroidal Chaos, Phys. D, 1991, vol. 49, no. 3, pp. 387-475.
    • (1991) Phys. D , vol.49 , Issue.3 , pp. 387-475
    • Baesens, C.1    Guckenheimer, J.2    Kim, S.3    Mackay, R.S.4
  • 67
    • 33747126823 scopus 로고
    • Perturbations of Translations in the Two-Dimensional Torus: The Case near Resonance
    • (Universidad de Zaragoza, Jaca, Spain, 1983), Zaragoza
    • Simó, C., Perturbations of Translations in the Two-Dimensional Torus: The Case near Resonance, Proceedings VI CEDYA (Universidad de Zaragoza, Jaca, Spain, 1983), Zaragoza, 1984.
    • (1984) Proceedings VI CEDYA
    • Simó, C.1
  • 68
    • 78149327844 scopus 로고    scopus 로고
    • Survey of Strong Normal-Internal k: L Resonances in Quasi-Periodically Driven Oscillators for l = 1, 2, 3
    • G. Gaeta, R. Vitolo, and S. Walcher (Eds.), Hackensack, NJ: World Sci. Publ
    • Broer, H. W., van Dijk, R., and Vitolo, R., Survey of Strong Normal-Internal k: l Resonances in Quasi-Periodically Driven Oscillators for l = 1, 2, 3, Proceedings SPT 2007, Internat. Conf. on Symmetry and Perturbation Theory (Otranto (Italy), 2-9 June 2007), G. Gaeta, R. Vitolo, S. Walcher (Eds.), Hackensack, NJ: World Sci. Publ., 2008, pp. 45-55.
    • (2008) Proceedings SPT 2007, Internat. Conf. On Symmetry and Perturbation Theory (Otranto (Italy), 2-9 June 2007) , pp. 45-55
    • Broer, H.W.1    van Dijk, R.2    Vitolo, R.3
  • 69
    • 0142239172 scopus 로고    scopus 로고
    • Semi-Local Analysis of the k: 1 and k: 2 Resonances in Quasi-Periodically Forced Systems
    • H. W. Broer, B. Krauskopf, and G. Vegter (Eds.), Bristol: Inst. Phys
    • Wagener, F. O. O., Semi-Local Analysis of the k: 1 and k: 2 Resonances in Quasi-Periodically Forced Systems, Global Analysis of Dynamical Systems: Festschrift Dedicated to Floris Takens for His 60th Birthday, H. W. Broer, B. Krauskopf, G. Vegter (Eds.), Bristol: Inst. Phys., 2001, pp. 113-129.
    • (2001) Global Analysis of Dynamical Systems: Festschrift Dedicated to Floris Takens for His 60th Birthday , pp. 113-129
    • Wagener, F.O.O.1
  • 70
    • 14844309663 scopus 로고    scopus 로고
    • KAM theory without Action-Angle Variables
    • de la Llave, R., González, A., Jorba, À., and Villanueva, J., KAM theory without Action-Angle Variables, Nonlinearity, 2005, vol. 18, no. 2, pp. 855-895.
    • (2005) Nonlinearity , vol.18 , Issue.2 , pp. 855-895
    • de la Llave, R.1    González, A.2    Jorba3    Villanueva, J.4
  • 71
    • 34548493255 scopus 로고    scopus 로고
    • Parametric Smoothness and Self-Scaling of the Statistical Properties of a Minimal Climate Model: What beyond the Mean Field Theories?
    • Lucarini, V., Speranza, A., and Vitolo, R., Parametric Smoothness and Self-Scaling of the Statistical Properties of a Minimal Climate Model: What beyond the Mean Field Theories? Phys. D, 2007, vol. 234, no. 2, pp. 105-123.
    • (2007) Phys. D , vol.234 , Issue.2 , pp. 105-123
    • Lucarini, V.1    Speranza, A.2    Vitolo, R.3
  • 72
    • 33747060717 scopus 로고    scopus 로고
    • Direct Numerical Simulations of Bifurcations in an Air-Filled Rotating Baroclinic Annulus
    • Randriamampianina, A., Früh, W.-G., Maubert, P., and Read, P. L., Direct Numerical Simulations of Bifurcations in an Air-Filled Rotating Baroclinic Annulus J. Fluid Mech., 2006, vol. 561, pp. 359-389.
    • (2006) J. Fluid Mech. , vol.561 , pp. 359-389
    • Randriamampianina, A.1    Früh, W.-G.2    Maubert, P.3    Read, P.L.4
  • 73
    • 48149094941 scopus 로고    scopus 로고
    • Flow Transitions Resembling Bifurcations of the Logistic Map in Simulations of the Baroclinic Rotating Annulus
    • Young, R. M. B. and Read, P. L., Flow Transitions Resembling Bifurcations of the Logistic Map in Simulations of the Baroclinic Rotating Annulus, Phys. D, 2008, vol. 237, no. 18, pp. 2251-2262.
    • (2008) Phys. D , vol.237 , Issue.18 , pp. 2251-2262
    • Young, R.M.B.1    Read, P.L.2
  • 74
    • 70350738968 scopus 로고    scopus 로고
    • On the Computation of Reducible Invariant Tori on a Parallel Computer
    • Jorba, À. and Olmedo, E., On the Computation of Reducible Invariant Tori on a Parallel Computer, SIAM J. Appl. Dyn. Syst., 2009, vol. 8, no. 4, pp. 1382-1404.
    • (2009) SIAM J. Appl. Dyn. Syst. , vol.8 , Issue.4 , pp. 1382-1404
    • Jorba1    Olmedo, E.2
  • 75
    • 0002761467 scopus 로고
    • Formal Normal Forms Theorems for Vector Fields and Some Consequences for Bifurcations in the Volume Preserving Case
    • Lecture Notes in Math, A. Dold and B. Eckmann (Eds.), Berlin-New York: Springer
    • Broer, H. W., Formal Normal Forms Theorems for Vector Fields and Some Consequences for Bifurcations in the Volume Preserving Case, Dynamical Systems and Turbulence, Warwick 1980 (Coventry, 1979/1980), A. Dold and B. Eckmann (Eds.), Lecture Notes in Math., vol. 898, Berlin-New York: Springer, 1980, pp. 54-74.
    • (1980) Dynamical Systems and Turbulence, Warwick 1980 (Coventry, 1979/1980) , vol.898 , pp. 54-74
    • Broer, H.W.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.