2019/02/06 by Hildebrando M. Rodrigues, Rodrigues, Hildebrando M., J. Solà‐Morales +1
Engineering · Mathematics · #35B35 #37C75 #43D20 #47A10 #Advanced Differential Equations and Dynamical Systems #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.1902.02111
openalex publication_date 2019/02/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The purpose of this paper is to present an example of a C1 (in the Fréchet sense) discrete dynamical system in a infinite-dimensional separable Hilbert space for which the origin is an exponentially asymptotically stable fixed point, but such that its derivative at the origin has spectral radius larger than unity, and this means that the origin is unstable in the sense of Lyapunov for the linearized system. The possible existence or not of an example of this kind has been an open question until now, to our knowledge. The construction is based on a classical example in Operator Theory due to Kakutani.