Autor(es)

Sola-Morales, B. J. ; Rodrigues, Hildebrando M.

• Tipo de documento: Artigo Científico
• Fonte: Journal of Dynamics and Differential Equations; v. 36, n. SUPPL 1, p. 9-pg., 2024-02-01.

Resumo

The purpose of this paper is to present an example of an Ordinary Differential Equation x = F(x)in the in.nite-dimensional Hilbert space 2 with F being of class Cl in the Frechet sense, such that the origin is an asymptotically stable equilibrium point but the spectrum of the linearized operator DF(0)intersects the half-plane (z)>0. The possible existence or not of an example of this kind has been an open question until now, to our knowledge. An analogous example, but of a non-invertible map instead of a.ow de.ned by an ODE was recently constructed by the authors in Rodrigues and Sold-Morales (J. Differ. Equ. 269:1349-1359, 2020). The two examples use different techniques, but both are based on a classical example in Operator Theory due to S. Kakutani. (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