Hopf bifurcation from nonperiodic solutions of differential equations. I: Linear theory

DOI10.1007/BF01047830zbMath0684.34038OpenAlexW2073107291MaRDI QIDQ1825343

Russell A. Johnson

Publication date: 1989

Published in: Journal of Dynamics and Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf01047830

zbMATH Keywords

Hopf bifurcationexponential dichotomyrotation number

Mathematics Subject Classification ID

Growth and boundedness of solutions to ordinary differential equations (34C11) General theory for ordinary differential equations (34A99) Dynamical systems and ergodic theory (37-XX)

Related Items (10)

Bifurcations in non-autonomous scalar equations ⋮ On the Lyapunov exponent of certain \(SL (2,\mathbb R)\)-valued cocycles. II ⋮ On \({SL(2, \mathbb R)}\) valued smooth proximal cocycles and cocycles with positive Lyapunov exponents over irrational rotation flows ⋮ A biography of Russell A. Johnson ⋮ Hyperbolicity and integral expression of the Lyapunov exponents for linear cocycles ⋮ Taylor approximation of invariant fiber bundles for nonautonomous difference equations ⋮ Taylor approximation of integral manifolds ⋮ Nonautonomous bifurcation scenarios in SIR models ⋮ Adaptive data distribution for concurrent continuation ⋮ Towards a bifurcation theory for nonautonomous difference equations

Cites Work

• Exponential dichotomy, rotation number, and linear differential operators with bounded coefficients
• The Floquet exponent for two-dimensional linear systems with bounded coefficients
• The rotation number for almost periodic potentials
• Existence of dichotomies and invariant splittings for linear differential systems. I
• On almost reducible systems with almost periodic coefficients
• Existence of dichotomies and invariant splittings for linear differential systems. III
• A spectral theory for linear differential systems
• Dichotomies in stability theory
• Occurrence of strange Axiom A attractors near quasi periodic flows on \(T^m\), \(m\geq 3\)
• Bifurcation of higher dimensional Tori
• Asymptotic cycles
• On the nature of turbulence
• Remarks on Linear Differential Systems with Measurable Coefficients
• The algebraic-geometric AKNS potentials
• Ergodic Properties of Linear Dynamical Systems
• Exponential Dichotomies for Almost Periodic Equations
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