Citation for published version (APA): Holtman, S-J. (2009). Dynamics and geometry near resonant bifurcations Groningen: s.n.

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1 University of Groningen Dynamics and geometry near resonant bifurcations Holtman, Sijbo-Jan IMPORTANT NOTE: You are advised to consult the publisher's version (publisher's PDF) if you wish to cite from it. Please check the document version below. Document Version Publisher's PDF, also known as Version of record Publication date: 2009 Link to publication in University of Groningen/UMCG research database Citation for published version (APA): Holtman, S-J. (2009). Dynamics and geometry near resonant bifurcations Groningen: s.n. Copyright Other than for strictly personal use, it is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), unless the work is under an open content license (like Creative Commons). Take-down policy If you believe that this document breaches copyright please contact us providing details, and we will remove access to the work immediately and investigate your claim. Downloaded from the University of Groningen/UMCG research database (Pure): For technical reasons the number of authors shown on this cover page is limited to 10 maximum. Download date:

2 Bibliography [Arn82] [Arn93] [BCKV93] [BCKV95] V.I. Arnol d. Geometrical Methods in the Theory of Ordinary Differential Equations. Springer Berlin, V.I. Arnol d, editor. Dynamical systems VI: Singularity theory I, volume 6 of Ecyclopaedia of Mathematical Sciences. Springer-Verlag, Berlin, H.W. Broer, S.N. Chow, Y. Kim, and G. Vegter. A normally elliptic hamiltonian bifurcation. ZAMP, pages , H.W. Broer, S.N. Chow, Y. Kim, and G. Vegter. The hamiltonian doublezero eigenvalue. In W.F. Langford and W. Nagata, editors, Normal Forms and Homoclinic Chaos (Waterloo 1992), volume 4, pages Fields Institute Communications, [BdBGV81] J.G. Blom, R. de Bruin, J. Grasman, and J.G. Verwer. Forced prey-predator oscillations. Journal of Mathematical Biology, 12: , [BGV03] [BGV07] [BHLV98a] H.W. Broer, M. Golubitsky, and G. Vegter. The geometry of resonance tongues: A singularity approach. Nonlinearity, 16: , H.W. Broer, M. Golubitsky, and G. Vegter. Geometry of resonance tongues. Singularity Theory. Proceedings of the 2005 Marseille Singularity School and Conference, pages , H.W. Broer, I. Hoveijn, G.A. Lunter, and G. Vegter. Equivariant singularity theory with distinguished parameters, two case studies of resonant Hamiltonian systems. Physica D, 112:64 80, [BHLV98b] H.W. Broer, I. Hoveijn, G.A. Lunter, and G. Vegter. Resonance in a springpendulum: algorithms for equivariant singularity theory. Nonlinearity, 11:1 37, [BHLV03] H.W. Broer, I. Hoveijn, G.A. Lunter, and G. Vegter. Bifurcations in Hamiltonian systems: Computing singularities by Gröbner bases. Springer LNM 1806, ISBN

3 128 Bibliography [BHV08] [BL95] [BNR + 07] [BNRS06] [BR01] [Brö75] [Bro09] [BS98] [BS00] [BST98] [BSV02] [BSV08] [BV92] H.W. Broer, S.J. Holtman, and G. Vegter. Recognition of the bifurcation type of resonance in mildly degenerate Hopf-Neĭmark-Sacker families. Nonlinearity, 21: , H.W. Broer and M. Levi. Geometrical aspects of stability theory for Hill s equations. Arch. Rational Mech. Anal., 131: , H.W. Broer, V. Naudot, R. Roussarie, K. Saleh, and F.O.O. Wagener. Organising centres in the semi-global analysis of dynamical systems. Int. J. Appl. M. Stat., 12(D7), H.W. Broer, V. Naudot, R. Roussarie, and K. Saleh. A predator-prey model with non-monotonic response function. Regular and Chaotic Dynamics, 11: , H.W. Broer and R. Roussarie. Exponential confinement of chaos in the bifurcation set of real analytic diffeomorphisms. In H.W. Broer, B. Krauskopf, and G. Vegter, editors, Global Analysis of Dynamical systems, Festschrift dedicated to Floris Takens for his 60th birthday, pages IOP, Bristol and Philadelphia, T. Bröcker. Differential Germs and Catastrophes. London Mathematical Society Lecture Note Series. Cambridge University Press, Cambridge, H.W. Broer. Normal forms in perturbation theory. In R. Meyers, editor, Encyclopædia of Complexity and System Science. Springer-Verlag, H.W. Broer and C. Simo. Hill s equation with quasi-periodic forcing: resonance tongues, instability pockets and global phenomena. Bol. Soc. Bras. Mat., 29: , H.W. Broer and C. Simo. Resonance tongues in Hill s equations: a geometric approach. J. Diff. Eqns., 166: , H.W. Broer, C. Simó, and J.C. Tatjer. Towards global models near homoclinic tangencies of dissipative diffeomorphisms. Nonlinearity, 11: , H.W. Broer, C. Simó, and R. Vitolo. Bifurcations and strange attractors in the lorenz-84 climate model with seasonal forcing. Nonlinearity, 15(4): , H.W. Broer, C. Simó, and R. Vitolo. The Hopf-saddle-node bifurcation for fixed points of 3D-diffeomorphisms: analysis of a resonance bubble. Phys. D, 237(13): , H.W. Broer and G. Vegter. Bifurcational aspects of parametric resonance. In Dynamics Reported, volume 1 of New Series, pages Springer-Verlag, 1992.

4 Bibliography 129 [BV08] [Che85a] [Che85b] [Che88] [Dev89] [DRSZ91] [DV94] [GH83] [GS88] [GSS85] H.W. Broer and G. Vegter. Generic Hopf-Neĭmarck-Sacker bifurcations in feedforward systems. Nonlinearity, 21: , A. Chenciner. Bifurcations de points fixes elliptiques, i. courbes invariantes. Publ. Math. IHES, 61:67 127, A. Chenciner. Bifurcations de points fixes elliptiques, ii. orbites périodiques et ensembles de cantor invariants. Invent. Math., 80:81 106, A. Chenciner. Bifurcations de points fixes elliptiques, iii. orbites périodiques de petites périodes et elimination résonnantes des couples de courbes invariantes. Publ. Math. IHES, 66:5 91, R.L. Devaney. An introduction to chaotic dynamical systems. Addison-Wesley, F. Dumortier, R. Rousarie, J. Sotomayor, and H. Zoladek. Bifurcations on planar vector fields. Springer-Verlag, A. Doelman and F. Verhulst. Bifurcations and strongly non-linear self-exited oscillations. Mathematical Methods in the Applied Sciences, 17: , J. Guckenheimer and P. Holmes. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer-Verlag, M. Golubitsky and D.G. Schaeffer. Singularities and Groups in Bifurcation Theory: Vol. II, volume 69 of Applied Mathematical Sciences. Springer-Verlag, New-York, M. Golubitsky, I.N. Stewart, and D.G. Schaeffer. Singularities and Groups in Bifurcation Theory: Vol. I, volume 51 of Applied Mathematical Sciences. Springer-Verlag, New-York, [GWdPL76] C.G. Gibson, K. Wirthmüller, A.A. du Plessis, and E.J.N. Looijenga. Topological Stability of Smooth Mappings. Springer-Verlag, Berlin, Lecture Notes in Mathematics, Vol [Hal80] J. Hale. Ordinary Differential Equations. Krieger, [HH81] [Hol] [Hum79] C. Holmes and P. Holmes. Second order averaging and bifurcations of subharmonics in Duffing s equation. Journal of Sound and Vibration, 78(2): , S.J. Holtman. Homepage. A. Hummel. Bifurcations of periodic points. PhD thesis, University of Groningen, 1979.

5 130 Bibliography [Ily08] [IY95] [JZ05] [Kif08] [Kra94] [Kuz95] [LM09] Y. Ilyashenko. Some open problems in real and complex dynamical systems. Nonlinearity, 21:T101 T107, Y. Ilyashenko and S. Yakovenko. Finite cyclicity of elementary polycycles in generic families. In Concerning the Hilbert 16th problem, volume 165 of Amer. Math. Soc. Transl. Ser. 2, pages Amer. Math. Soc., Providence, RI, A. Jorba and M. Zou. A software package for the numerical integration of ODEs by means of high-order Taylor methods. Experiment. Math., 14(1):99 117, Y. Kifer. Convergence, nonconvergence and adiabatic transitions in fully coupled averaging. Nonlinearity, 21:T27 T32, B. Krauskopf. Bifurcation sequences at 1:4 resonance: an inventory. Nonlinearity, 7: , Y.A. Kuznetsov. Elements of Applied Bifurcation Theory, volume 112 of Applied Mathematical Sciences. Springer-Verlag, Berlin and New-York, H.E. Lomeli and J.D. Meiss. Resonance zones and lobe volumes for exact volume-preserving maps. Nonlinearity, 22: , [Mou91] A. Mourtada. Cyclicité finie des polycycles hyperboliques de champs de vecteurs du plan. Algorithme de finitude. Ann. Inst. Fourier (Grenoble), 41(3): , [MP95] [MP96] R.P. McGehee and B.B. Peckham. Determining the global topology of resonance surfaces for periodically forced oscillator families. In W.F. Langford and W. Nagata, editors, Normal Forms and Homoclinic Chaos, volume 4 of Fields Institute Communications, pages AMS, R.P. McGehee and B.B. Peckham. Arnol d flames and resonance surface folds. Int. J. Bifurcations and Chaos, 6: , [Mun99] J.R. Munkres. Topology. Prentice Hall, [NPT83] [PFK95] [PK91] S.E. Newhouse, J. Palis, and F. Takens. Bifurcation and stability of families of diffeomorphisms. Publ.Math.IHES, 57:1 71, B.B. Peckham, C.E. Frouzakis, and I.G. Kevrekidis. Bananas and banana splits: a parametric degeneracy in the Hopf bifurcation for maps. SIAM J. Math. Anal., 26: , B.B. Peckham and I.G. Kevrekidis. Period doubling with higher-order degeneracies. SIAM J. Math. Anal., 22: , 1991.

6 Bibliography 131 [PK02] [PS96] [PT87] B.B. Peckham and I.G. Kevrekidis. Lighting Arnol d flames: Resonance in doubly forced periodic oscillators. Nonlinearity, 15: , T. Poston and I. Stewart. Catastrophe theory and its applications. Dover publications, Dover, J. Palis and F. Takens. Hyperbolicity and the creation of homoclinic orbits. Ann. Math., 125: , [Rey80] J. W. Reyn. Generation of limit cycles from separatrix polygons in the phase plane. In Geometrical approaches to differential equations (Proc. Fourth Scheveningen Conf., Scheveningen, 1979), volume 810 of Lecture Notes in Math., pages Springer, Berlin, [Rou86] [Sim90] [SKT04] [SVM07] [Tak74a] R. Roussarie. On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields. Bol. Soc. Brasil. Mat., 17(2):67 101, C. Simó. On the analytical and numerical approximation of invariant manifolds. In Daniel Benest and Claude Froeschlé, editors, Méthodes Modernes de la Mecánique Céleste (Course given at Goutelas, France, 1989), pages Editions Frontières, M. Siewe, F.M. Kameni, and C. Tchawona. Resonant oscillation and homoclinic bifurcation in a Φ 6 -van der pol oscillator. Chaos, Solitons and Fractals, 24(4): , J.A. Sanders, F. Verhulst, and J. Murdock. Averaging Methods in Nonlinear Dynamical Systems, volume 59 of Applied Mathematical Sciences. Springer, F. Takens. Forced oscillations and bifurcations. In Applications of Global Analysis I, volume 3, pages Communications of the Mathematical Institute of the University of Utrecht, Reprinted in: H.W. Broer, B. Krauskopf and G. Vegter, editors, Global Analysis of Dynamical Systems. Festschrift Dedicated to Floris Takens for his 60th Birthday (Leiden, 2001), Inst. Physics, Bristol (2001), [Tak74b] F. Takens. Singularities of vector fields. Publ. Math. IHES, 42:48 100, [Tho75] [Van92] R. Thom. Structural Stability and Morphogenesis. Benjamin-Addison Wesley, New-York, A. Vanderbauwhede. Branching of periodic solutions in time-reversible systems. In H.W. Broer and F. Takens, editors, Geometry and Analysis in Non-linear Dynamics, volume 222 of Pitman Research Notes in Mathematics, pages Pitman London, 1992.

7 132 Bibliography [vdpvdm27] B. van der Pol and J. van der Mark. Frequency demultiplication. Nature, 120: , [Wol08] [Yag96] Wolfram Research, Inc. Mathematica, Version 7.0. Wolfram Research, Inc., Champaign, Illinois, K. Yagasaki. Second-order averaging and Melnikov analyses for forced nonlinear oscillators. Journal of Sound and Vibration, 190(4): , 1996.

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