Central limit theorem for generalized Weierstrass functions

Autor(es)

de Lima, Amanda ^[1] ; Smania, Daniel ^[1]

Afiliação do(s) autor(es)

^[1] ICMC USP, Dept Matemat, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Stochastics and Dynamics; v. 19, n. 1 FEB 2019.
• Citações Web of Science: 0

Resumo

Let f : S-1 -> S-1 be a C2+epsilon expanding map of the circle and let v : S-1 -> R be a C1+epsilon function. Consider the twisted cohomological equation v = alpha o f -Df . alpha, which has a unique bounded solution alpha. We show that a is either C(1+epsilon )or continuous but nowhere differentiable. If a is nowhere differentiable then the Newton quotients of alpha, after an appropriated normalization, converges in distribution (with respect to the unique absolutely continuous invariant probability of f) to the normal distribution. In particular, alpha is not a Lipschitz continuous function on any subset with positive Lebesgue measure. (AU)

• Processo FAPESP: 10/17419-6 - Famílias transversais de transformações expansoras por pedaços
• Beneficiário: Amanda de Lima
• Modalidade de apoio: Bolsas no Brasil - Doutorado
• Processo FAPESP: 17/06463-3 - Aspectos probabilísticos e algébricos de sistemas dinâmicos suaves
• Beneficiário: Ali Tahzibi
• Modalidade de apoio: Auxílio à Pesquisa - Temático