Holmes, Philip; Marsden, Jerrold Bifurcation to divergence and flutter in flow-induced oscillations: An infinite dimensional analysis. (English) Zbl 0385.93028 Automatica 14, 367-384 (1978). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 43 Documents MSC: 93C20 Control/observation systems governed by partial differential equations 93C10 Nonlinear systems in control theory 35B32 Bifurcations in context of PDEs 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 37G99 Local and nonlocal bifurcation theory for dynamical systems × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Dowell, E. H., Nonlinear oscillations of a fluttering plate, AIAA J., 4, 7, 1267-1275 (1966) [2] Dowell, E. H., Aeroelasticity of Plates and Shells (1975), Noordhoff: Noordhoff Leyden · Zbl 0306.73039 [3] Holmes, P. J., Bifurcations to divergence and flutter in flow-induced oscillations: a finite dimensional analysis, J. Sound Vibration, 53, 4, 471-503 (1977) · Zbl 0363.73059 [4] Marsden, J. E.; McCracken, M., The Hopf Bifurcation and its Applications, Springer Applied Math Sciences No. 19 (1976), New York · Zbl 0346.58007 [5] Takens, F., Forced Oscillations and Bifurcations (1974), Communication 3 of the Maths Institute, Rijksuniversiteit: Communication 3 of the Maths Institute, Rijksuniversiteit Utrecht [6] Holmes, P. J.; Marsden, J. E., Qualitative analysis of a class of partial differential equations describing flutter (1978), (in preparation) [7] Parks, P. C., A stability criterion for a panel flutter problem via the second method of Liapunov, (Hale, J. K.; La Salle, J. P., Differential Equations and Dynamical Systems (1966), Academic Press: Academic Press New York) · Zbl 0111.28303 [8] Kato, T., Perturbation Theory for Linear Operators (1976), Springer · Zbl 0342.47009 [9] Segal, I., Nonlinear semigroups, Ann. Math., 78, 339-364 (1963) · Zbl 0204.16004 [10] Ball, J. M., Stability theory for an extensible beam, J. Diff. Eqns, 14, 399-418 (1973) · Zbl 0247.73054 [11] Hirsch, M. W.; Pugh, C.; Shub, M., Invariant Manifolds, Springer Lecture Notes No. 583 (1977), New York · Zbl 0355.58009 [12] Ball, J. M.; Carr, J., Decay to zero in critical cases of second order ordinary differential equations of Duffing type, Archs Rat. Mech. Anal., 63, 47-57 (1976) · Zbl 0356.34041 [13] Hopf, E., Abzweigung einer periodischen Lösung von einer stationaren Lösung eines Differentialsystems, Ber. Maths. Phys. Sachsische Akad. Wiss. Leipzig, 94, 1-22 (1942), (See [4], Chapter 5 for translation) · Zbl 0063.02065 [14] B. HassardY.-H. WanJ. Math. Anal. Applic.; B. HassardY.-H. WanJ. Math. Anal. Applic. · Zbl 0435.34034 [15] Henry, D., Geometric Theory of Parabolic Equations (1975), University of Kentucky lecture notes [16] Kelley, A., The stable, center-stable, center, center-unstable and unstable manifolds, J. Diff. Eqns, 3, 546-570 (1967) · Zbl 0173.11001 [17] Kopell, N.; Howard, L. N., Bifurcations and trajectories joining critical points, Adv. Math., 18, 306-358 (1976) · Zbl 0361.34026 [18] Holmes, P. J.; Rand, D. A., Identification of vibrating systems by generic modelling, Institute of Sound and Vibration Research Technical Report No. 79 (1975), Southampton [19] Takens, F., Introduction to global Analysis (1973), Communication 2 of the Maths Institutie Rijksuniversiteit: Communication 2 of the Maths Institutie Rijksuniversiteit Utrecht [20] F. TAKENS: Singularities of vectorfields. Publs Inst. ht. Etud. scient. 43, 47-100.; F. TAKENS: Singularities of vectorfields. Publs Inst. ht. Etud. scient. 43, 47-100. · Zbl 0279.58009 [21] Sotomayor, J., Generic one parameter families of vector fields on two dimensional manifolds, Publs Inst. ht. Etud. scient., 43, 5-46 (1974) · Zbl 0279.58008 [22] Arnold́, V. I., Lectures on bifurcations in versal families, Russ. Math. Surv., 27, 54-123 (1972) · Zbl 0264.58005 [23] Andronov, A. A.; Leontovich, E. A.; Gordon, I. I.; Maier, A. G., Theory of Bifurcations of Dynamic Systems on a Plane (1973), Wiley: Wiley New York, (trans. D. Louvish) · Zbl 0282.34022 [24] Thom, R., Stabilité Structurelle et Morphogénèse (1972), Benjamin: Benjamin Reading, Mass, (English version by D. H. Fowler, Benjamin, 1975) [25] Chillingworth, D. R.J., Differential Topology with a View to Applications (1976), Pitman · Zbl 0336.58001 [26] Chillingworth, D. R.J., The catastrophe of a buckling beam, (Manning, A. K., Warwick Dynamical Systems. Warwick Dynamical Systems, Springer Lecture Notes No. 468 (1974), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0172.48801 [27] Chillingworth, D. R.J.; Furness, P. M., A model for reversals of the earth’s magnetic field, (Manning, A. K., Warwick Dynamical Systems (1974), Springer-Verlag: Springer-Verlag Berlin) · Zbl 0307.58006 [28] Sel’kov, E. E., Nonlinearity of multienzyme systems, (Hemter, H. C.; Hess, B., Analysis and Simulation of Biochemical Systems (1972), North Holland: North Holland Amsterdam) [29] Smale, S., Differentiable dynamical systems, Bull. Am. Math. Soc., 73, 747-817 (1967) · Zbl 0202.55202 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.