An example on Lyapunov stability and linearization

DOI10.1016/j.jde.2020.01.027zbMath1451.37033arXiv1902.02111OpenAlexW3003855000MaRDI QIDQ1989438

Hildebrando M. Rodrigues, Joan Solà-Morales

Publication date: 22 April 2020

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

Full work available at URL: https://arxiv.org/abs/1902.02111

zbMATH Keywords

fixed pointslinearizationLyapunov stabilityseparable Hilbert space

Mathematics Subject Classification ID

Spectrum, resolvent (47A10) Fixed points and periodic points of dynamical systems; fixed-point index theory; local dynamics (37C25) Stability theory for smooth dynamical systems (37C75) Operators on Hilbert spaces (general) (47B02)

Related Items (3)

Stability problems in nonautonomous linear differential equations in infinite dimensions ⋮ A new example on Lyapunov stability ⋮ Linearized stability in the context of an example by Rodrigues and Solà-Morales

Cites Work

• Known results and open problems on \(\mathcal C^1\) linearization in Banach spaces
• Linearization of class \(C^{1}\) for contractions on Banach spaces
• Invertible contractions and asymptotically stable ODE's that are not \({\mathcal C}^1\)-linearizable
• Geometric theory of semilinear parabolic equations
• Stability theory and the existence of periodic solutions and almost periodic solutions
• On nonlinear stabilization of linearly unstable maps
• The converse of the theorem on stability by the first approximation for difference equations.
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