New rotation sets in a family of torus homeomorphisms

Autor(es)

Boyland, Philip ^[1] ; de Carvalho, Andre ^[2] ; Hall, Toby ^[3]

Afiliação do(s) autor(es)

^[1] Univ Florida, Dept Math, 372 Little Hall, Gainesville, FL 32611 - USA

^[2] Univ Sao Paulo, IME, Dept Matemat Aplicada, Rua Matao 1010, Cidade Univ, BR-05508090 Sao Paulo, SP - Brazil

^[3] Univ Liverpool, Dept Math Sci, Liverpool L69 7ZL, Merseyside - England

• Tipo de documento: Artigo Científico
• Fonte: INVENTIONES MATHEMATICAE; v. 204, n. 3, p. 895-937, JUN 2016.
• Citações Web of Science: 6

Resumo

We construct a family of homeomorphisms of the two-torus isotopic to the identity, for which all of the rotation sets can be described explicitly. We analyze the bifurcations and typical behavior of rotation sets in the family, providing insight into the general questions of toral rotation set bifurcations and prevalence. We show that there is a full measure subset of {[}0, 1], consisting of infinitely many mutually disjoint non-trivial closed intervals, on each of which the rotation set mode locks to a constant polygon with rational vertices; that the generic rotation set in the Hausdorff topology has infinitely many extreme points, accumulating on a single totally irrational extreme point at which there is a unique supporting line; and that, although varies continuously with t, the set of extreme points of does not. The family also provides examples of rotation sets for which an extreme point is not represented by any minimal invariant set, or by any directional ergodic measure. (AU)

• Processo FAPESP: 11/17581-0 - Métodos topológicos em dinâmica de superfícies: da família de Hénon a conjuntos de rotação no toro
• Beneficiário: André Salles de Carvalho
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional
• Processo FAPESP: 10/09667-0 - Métodos topológicos em dinâmica em baixas dimensões
• Beneficiário: André Salles de Carvalho
• Modalidade de apoio: Auxílio à Pesquisa - Pesquisador Visitante - Internacional