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(Reference retrieved automatically from Web of Science through information on FAPESP grant and its corresponding number as mentioned in the publication by the authors.)

Central limit theorem for generalized Weierstrass functions

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de Lima, Amanda [1] ; Smania, Daniel [1]
Total Authors: 2
[1] ICMC USP, Dept Matemat, Caixa Postal 668, BR-13560970 Sao Carlos, SP - Brazil
Total Affiliations: 1
Document type: Journal article
Source: Stochastics and Dynamics; v. 19, n. 1 FEB 2019.
Web of Science Citations: 0

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)

FAPESP's process: 10/17419-6 - Transversal families of piecewise expanding maps
Grantee:Amanda de Lima
Support type: Scholarships in Brazil - Doctorate
FAPESP's process: 17/06463-3 - Probabilistic and algebraic aspects of smooth dynamical systems
Grantee:Ali Tahzibi
Support type: Research Projects - Thematic Grants