zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
The Hopf bifurcation theorem in infinite dimensions. (English) Zbl 0385.34020

MSC:
34C25Periodic solutions of ODE
34A99General theory of ODE
34G10Linear ODE in abstract spaces
References:
[1]Alexander, J.C. & J.A. Yorke, Global bifurcation of periodic orbits. Preprint, 1976.
[2]Chafee, N., The bifurcation of one or more closed orbits from an equilibrium point of an autonomous differential equation. J. Differential Equations, 4, 661-679 (1968). · Zbl 0169.11301 · doi:10.1016/0022-0396(68)90015-6
[3]Crandall, M.G. & P.H. Rabinowitz, Bifurcation from simple eigenvalues. J. Functional Anal., 8, 321-340 (1971). · Zbl 0219.46015 · doi:10.1016/0022-1236(71)90015-2
[4]Crandall, M.G. & P.H. Rabinowitz, Bifurcation, perturbation of simple eigenvalues, and linearized stability. Arch. Rational Mech. Analysis, 52, 161-180 (1973). · Zbl 0275.47044 · doi:10.1007/BF00282325
[5]Crandall, M.G. & P.H. Rabinowitz, The Hopf Bifurcation Theorem. TSR 1604 (1976), Mathematics Research Center, University of Wisconsin, Madison.
[6]Crandall, M.G. & P.H. Rabinowitz, The principle of exchange of stability. Proceedings of the International Symposium on Dynamical Systems, Gainsville, Florida, 1976 (to appear).
[7]Fife, P.C., Branching phenomena in fluid dynamics and chemical reaction-diffusion theory. Proc. Sym. ?Eigenvalues of Nonlinear Problems?, Edizioni Cremonese Rome, 23-83, 1974.
[8]Friedman, A., Partial Differential Equations. Holt, Rinehart and Winston, Inc., New York, 1969.
[9]Hartman, P., Ordinary Differential Equations. John Wiley, New York, 1964.
[10]Henry, D., Geometric theory of semilinear parabolic equations, University of Kentucky Lecture Notes, 1974.
[11]Henry, D., Perturbation problems. Northwestern University Lecture Notes, 1974.
[12]Hopf, E., Abzweigung einer periodischen Lösung von einer stationären Lösung eines Differentialsystems, Ber. Math.-Phys. Kl. Sächs. Akad. Wiss. Leipzig, 94, 3-22 (1942).
[13]Iooss, G., Existence et stabilité de la solution périodiques secondaire intervenant dans les problèmes d’evolution du type Navier-Stokes. Arch. Rational Mech. Analysis 47, 301-329 (1972). · Zbl 0258.35057 · doi:10.1007/BF00281637
[14]Iooss, G., Bifurcation et Stabilite. Cours de 3 ème cycle, 1973-74, Orsay.
[15]Iudovich, V.I., The onset of auto-oscillations in a fluid. Prikl. Mat. Mek., 35, 638-655 (1971).
[16]Iudovich, V.I., Investigation of auto-oscillations of a continuous medium occuring at loss of stability of a stationary mode. Prikl. Mat. Mek., 36, 450-459 (1972).
[17]Ize, G., Bifurcation global de orbitas periodicas. Preprint, 1976.
[18]Joseph, D.D., Stability of Fluid Motions, Springer, Berlin-Heidelberg-New York, 1976.
[19]Joseph, D.D., & D.A. Nield, Stability of bifurcating time periodic and steady solutions of arbitrary amplitude. Preprint, 1976.
[20]Joseph, D.D., & D.H. Sattinger, Bifurcating time periodic solutions and their stability. Arch. Rational Mech. Anal., 45, 79-109 (1972). · Zbl 0239.76057 · doi:10.1007/BF00253039
[21]Marsden, J., The Hopf bifurcation for nonlinear semigroups. Bull. Amer. Math. Soc., 79, 537- 541 (1973). · Zbl 0262.76031 · doi:10.1090/S0002-9904-1973-13191-X
[22]Marsden, J., & M. McCracken, The Hopf Bifurcation and its Applications. Springer Applied Mathematical Sciences Lecture Notes Series, Vol. 19, 1976.
[23]Poore, A.B., On the theory and application of the Hopf-Friedrichs bifurcation theory. Preprint, 1976.
[24]Ruelle, D., & F. Takens, On the nature of turbulence. Comm. Math. Phys., 20, 167-192 (1971). · Zbl 0223.76041 · doi:10.1007/BF01646553
[25]Sattinger, D.H., Bifurcation of periodic solutions of the Navier-Stokes equations. Arch. Rational Mech. Analysis, 41, 66-80 (1971). · Zbl 0222.76022 · doi:10.1007/BF00250178
[26]Sattinger, D.H., Topics in Stability and Bifurcation Theory, Lecture Notes in Mathematics No. 309. Springer, New York, 1973.
[27]Schmidt, D.S., Hopf’s bifurcation theorem and the center theorem of Liapunov. Preprint, 1976.
[28]Weinberger, H.F., The stability of solutions bifurcating from steady or periodic solutions. Proceedings of the International Symposium on Dynamical Systems, Gainsville Florida, 1976.