| Texto completo | |
| Autor(es): |
Garibaldi, Eduardo
;
Petite, Samuel
;
Thieullen, Philippe
Número total de Autores: 3
|
| Tipo de documento: | Artigo Científico |
| Fonte: | ANNALES HENRI POINCARE; v. 18, n. 9, p. 2905-2943, SEP 2017. |
| Citações Web of Science: | 2 |
| Resumo | |
The Frenkel-Kontorova model describes how an infinite chain of atoms minimizes the total energy of the system when the energy takes into account the interaction of nearest neighbors as well as the interaction with an exterior environment. An almost periodic environment leads to consider a family of interaction energies which is stationary with respect to a minimal topological dynamical system. We focus, in this context, on the existence of calibrated configurations (a notion stronger than the standard minimizing condition). In any dimension and for any continuous superlinear interaction energies, we exhibit a set, called projected Mather set, formed of environments that admit calibrated configurations. In the one-dimensional setting, we then give sufficient conditions on the family of interaction energies that guarantee the existence of calibrated configurations for every environment. The main mathematical tools for this study are developed in the frameworks of discrete weak KAM theory, Aubry-Mather theory and spaces of Delone sets. (AU) | |
| Processo FAPESP: | 09/17075-8 - Quasecristais e Teoria de Aubry-Mather |
| Beneficiário: | Eduardo Garibaldi |
| Modalidade de apoio: | Auxílio à Pesquisa - Regular |