Abstract Bifurcation Theorems and Applications to Dynamical Systems with Resonant Eigenvalues

DOI10.1007/978-1-4614-7333-6_38zbMath1326.47074OpenAlexW2101508835MaRDI QIDQ5248433

Vladimir Jacimovic

Publication date: 7 May 2015

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/978-1-4614-7333-6_38

zbMATH Keywords

Fredholm operatorsHopf invariantAndronov-Hopf bifurcationabstract integral equations

Mathematics Subject Classification ID

Applications of operator theory to differential and integral equations (47N20) Abstract bifurcation theory involving nonlinear operators (47J15) Abstract integral equations, integral equations in abstract spaces (45N05)

Cites Work

• Invariant manifolds for flows in Banach spaces
• New bifurcation theorems via the second-order optimality conditions
• Abstract Hopf bifurcation theorem and further extensions via second variation
• The Hopf bifurcation theorem in infinite dimensions
• The Hopf fibration --- seven times in physics
• Delay equations. Functional-, complex-, and nonlinear analysis
• Bifurcation from simple eigenvalues
• Bifurcation of periodic solutions of the Navier-Stokes equations
• Investigation of auto-oscillations of a continuous medium, occurring at loss of stability of a stationary mode
• The Hopf bifurcation for nonlinear semigroups
• Vector fields on spheres
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