Attractivity and Hopf bifurcation in Banach spaces

DOI10.1016/0022-247X(80)90223-1zbMath0452.35050MaRDI QIDQ1148462

S. H. Smith

Publication date: 1980

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

zbMATH Keywords

Hopf bifurcationcenter manifoldasymptotical stabilityinitial datacomparison argumentsone-parameter familieslocal attractivityAlekseev's representationbifurcating closed orbitsequations of parabolic type

Mathematics Subject Classification ID

Stability in context of PDEs (35B35) Periodic solutions to PDEs (35B10) Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs (35B05) Initial value problems for second-order parabolic equations (35K15) Bifurcations in context of PDEs (35B32)

Related Items (5)

Hopf bifurcation for fully nonlinear equations in Banach space ⋮ Attractivity and Hopf bifurcation in Banach spaces ⋮ Properties of Center Manifolds ⋮ Invariant manifolds for Volterra integral equations of convolution type ⋮ Hopf bifurcation calculations for functional differential equations

Cites Work

• Attractivity and Hopf bifurcation in Banach spaces
• Geometric theory of semilinear parabolic equations
• Sommes d'opérateurs linéaires et équations différentielles opérationnelles
• On the stabilizability problem in Banach space
• The Hopf bifurcation and its applications. With contributions by P. Chernoff, G. Childs, S. Chow, J. R. Dorroh, J. Guckenheimer, L. Howard, N. Kopell, O. Lanford, J. Mallet-Paret, G. Oster, O. Ruiz, S. Schecter, D. Schmidt, and S. Smale
• The Hopf bifurcation theorem in infinite dimensions
• Stability of unsteady motions in first approximation
• The bifurcation of one or more closed orbits from an equilibrium point of an autonomous differential system
• The stable, center-stable, center, center-unstable, unstable manifolds
• Non-linear semi-groups
• A bifurcation problem for a functional differential equation of finitely retarded type
• Transformation groups and bifurcation at multiple eigenvalues
• Attractivity and Hopf bifurcation
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