Uniform convergence rate for Birkhoff means of certain uniquely ergodic toral maps

Autor(es)

Klein, Silvius ^[1] ; Liu, Xiao-Chuan ^[2] ; Melo, Aline ^[1]

Afiliação do(s) autor(es)

^[1] Pontificia Univ Catolica Rio Janeiro PUG Rio, Dept Matemcit, Rio De Janeiro - Brazil

^[2] Univ Sao Paulo, Inst Matemat & Estat, R Matao 1010, Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Ergodic Theory and Dynamical Systems; v. 41, n. 11, p. 3363-3388, NOV 2021.
• Citações Web of Science: 0

Resumo

We obtain estimates on the uniform convergence rate of the Birkhoff average of a continuous observable over torus translations and affine skew product toral transformations. The convergence rate depends explicitly on the modulus of continuity of the observable and on the arithmetic properties of the frequency defining the transformation. Furthermore, we show that for the one-dimensional torus translation, these estimates are nearly optimal. (AU)

• Processo FAPESP: 18/03762-2 - Sistema dinâmicos topológicos em superfícies
• Beneficiário: Xiaochuan Liu
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado