An example on Lyapunov stability and linearization

Autor(es)

Rodrigues, Hildebrando M. ^[1] ; Sola-Morales, J. ^[2]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil

^[2] Univ Politecn Cataluna, Dept Matemat, Ave Diagonal 647, E-08028 Barcelona - Spain

• Tipo de documento: Artigo Científico
• Fonte: Journal of Differential Equations; v. 269, n. 2, p. 1349-1359, JUL 5 2020.
• Citações Web of Science: 0

Resumo

The purpose of this paper is to present an example of a C-1(in the Frechet 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. (C) 2020 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 18/05218-8 - Sistemas Dinâmicos não Lineares, Sincronização, Transformações, Equações Diferenciais e Aplicações.
• Beneficiário: Hildebrando Munhoz Rodrigues
• Modalidade de apoio: Auxílio à Pesquisa - Regular