Orbit structure of interval exchange transformations with flip

Autor(es)

Nogueira, Arnaldo ^[1] ; Pires, Benito ^[2] ; Troubetzkoy, Serge ^[3]

Afiliação do(s) autor(es)

^[1] Aix Marseille Univ 163, Inst Math Luminy, F-13288 Marseille 9 - France

^[2] Univ Sao Paulo, Dept Comp & Matemat, BR-14040901 Ribeirao Preto, SP - Brazil

^[3] Aix Marseille Univ, Inst Math Luminy, Ctr Phys Theor, Federat Rech Unites Math Marseille, F-13288 Marseille 9 - France

• Tipo de documento: Artigo Científico
• Fonte: Nonlinearity; v. 26, n. 2, p. 525-537, FEB 2013.
• Citações Web of Science: 7

Resumo

A sharp bound on the number of invariant components of an interval exchange transformation (IET) is provided. More precisely, it is proved that the number of periodic components n(per) and the number of minimal components n(min) of an interval exchange transformation of n intervals satisfy n(per) + 2n(min) <= n. Moreover, it is shown that almost all IETs are typical, that is, all have stable periodic components and all the minimal components are robust (i.e. persistent under almost all small perturbations). Finally, we find all the possible values for the integer vector (n(per), n(min)) for all typical IET of n intervals. (AU)

• Processo FAPESP: 09/02380-0 - Fluxos em superfícies e transformações de intercâmbio
• Beneficiário: Benito Frazao Pires
• Modalidade de apoio: Auxílio à Pesquisa - Jovens Pesquisadores
• Processo FAPESP: 08/02841-4 - Teoria topológica, geométrica e ergódica dos sistemas dinâmicos
• Beneficiário: Jorge Manuel Sotomayor Tello
• Modalidade de apoio: Auxílio à Pesquisa - Temático