This is a preview of subscription content, log in via an institution to check access.
Bibliography
N. Fenichel (1975), The orbit structure of the Hopf bifurcation problem. J. Diff. Eq. 17, 308–328.
G. Iooss (1972), Existence et stabilité de la solution périodique secondaire intervenant dans les problèmes d'évolution du type Navier-Stokes. Arch. Rational Mech. Anal. 47, 301–329.
G. Iooss (1974a), Bifurcation et stabilité. Pub. Math. d'Orsay No. 31.
G. Iooss (1974b), Bifurcation of a T-periodic flow towards an nT-periodic flow and their nonlinear stabilities. Arch. Mechaniki Stosovanej, 26, 5, 795–804.
G. Iooss (1975), Bifurcation of a periodic solution of the Navier-Stokes equations into an invariant torus. Arch. Rational Mech. Anal. 58, 1, 35–56.
G. Iooss (1977), Sur la deuxième bifurcation d'une solution stationnaire de systèmes du type Navier-Stokes. Arch. Rational Mech. Anal. 64, 4, 339–369.
V.I. Iudovich (1970), On the stability of forced oscillations of a liquid. Dokl. Acad. Nauk. S.S.S.R., 195, 292–295 (in Russian).
D. D. Joseph (1973), Remarks About Bifurcation and Stability of Quasi-periodic Solutions which Bifurcate from Periodic Solutions of the Navier-Stokes Equations. Lecture Notes in Maths. No. 322, 130–158. Berlin-Heidelberg-New York. Springer.
D. D. Joseph (1976), Stability of Fluid Motions I. Springer Tracts in Natural Philosophy. Berlin-Heidelberg-New York. Springer.
D. D. Joseph (1977), Factorization theorems, stability and repeated bifurcation. Arch. Rational Mech. Anal. 66, 99–118.
T. Kato (1966), Perturbation Theory for Linear Operators. Berlin-Heidelberg-New York. Springer.
O.E. Lanford III (1973), Bifurcation of Periodic Solutions into Invariant Tori: the work of Ruelle and Takens. Lecture Notes in Maths No 322, 159–192. Berlin-Heidelberg-New York: Springer.
G.S. Markman (1971), On the formation of convective cells periodic in time. M. Zh. G., 4, 109–119 (in Russian).
G. S. Markman (1972), Convective instability of a fluid layer in a modulated external force field. P.M.M., 36, 1, 152–157.
J. E. Marsden & M. McCracken (1976), The Hopf bifurcation and its applications. Applied Mathematical Sciences 19, New York-Heidelberg-Berlin: Springer.
D. Ruelle & F. Takens (1971), On the nature of turbulence. Comm. Maths. Phys. 20, 167–192.
R. J. Sacker (1964), On invariant surfaces and bifurcation of periodic solutions of ordinary differential equations. New York Univ. IMM-NYU, 333.
D. H. Sattinger (1972), Topics in Stability and Bifurcation Theory, Lecture Notes in Maths. No 309, Berlin-Heidelberg-New York: Springer.
C. S. Yih & C. H. Li (1972), Instability of unsteady flows or configurations. Part 2. Convective instability. J. Fluid Mech., 54, 1, 143–152.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Iooss, G., Joseph, D.D. Bifurcation and stability of nT-periodic solutions branching from T-periodic solutions at points of resonance. Arch. Rational Mech. Anal. 66, 135–172 (1977). https://doi.org/10.1007/BF00248631
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00248631