| Texto completo | |
| Autor(es): |
Addas-Zanata, Salvador
Número total de Autores: 1
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| Tipo de documento: | Artigo Científico |
| Fonte: | Ergodic Theory and Dynamical Systems; v. N/A, p. 31-pg., 2025-08-12. |
| Resumo | |
We consider twist diffeomorphisms of the torus, f: T-2 -> T-2, and their vertical rotation intervals, rho V(f)=[rho-(V),rho+(V)], where f is a lift of f to the vertical annulus or cylinder. We show that C (R)-generically, for any r >= 1 both extremes of the rotation interval are rational and locally constant under C-o-perturbations of the map. Moreover, when f is area-preserving, C (R)-generically, rho-(V),rho+(V). Also, for any twist map f, f a lift of f to the cylinder, if rho-(V)< rho+(V)= p/q, then there are two possibilities: either f(q) (.) - (0, p) maps a simple essential loop into the connected component of its complement which is below the loop, or it satisfies the curve intersection property. In the first case,rho+(V)= p/q in a Co-neighborhood of f, and in the second case, we show that rho rho-(V)< rho+(V)= p/q for all t > 0 (that is, the rotation interval is ready to grow). Finally, in the Cr-generic case, assuming that rho-(V)< rho+(V)= p/q, we present some consequences of the existence of the free loop for f(q) (.) - (0, p), related to the description and shape of the attractor-repeller pair that exists in the annulus. The case of a C (R)-generic transitive twist diffeomorphism (if such a thing exists) is also investigated. (AU) | |
| Processo FAPESP: | 23/07076-4 - Dinâmica e geometria em baixas dimensões |
| Beneficiário: | Fábio Armando Tal |
| Modalidade de apoio: | Auxílio à Pesquisa - Temático |