| Texto completo | |
| Autor(es): |
Rodrigues, Hildebrando M.
;
Sola-Morales, J.
Número total de Autores: 2
|
| Tipo de documento: | Artigo Científico |
| Fonte: | Journal of Dynamics and Differential Equations; v. N/A, p. 11-pg., 2021-03-01. |
| Resumo | |
The purpose of this paper is to present an example of an Ordinary Differential Equation x' = F(x) in the infinite-dimensional Hilbert space l(2) with F being of class C-1 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 R(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 flow defined by an ODE was recently constructed by the authors in Rodrigues and Sola-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 |