FLUCTUATIONS OF ERGODIC SUMS ON PERIODIC ORBITS UNDER SPECIFICATION

Autor(es)

Denker, Manfred ^[1] ; Senti, Samuel ^[2] ; Zhang, Xuan ^[3]

Afiliação do(s) autor(es)

^[1] Penn State Univ, Dept Math, University Pk, PA 16802 - USA

^[2] Univ Fed Rio de Janeiro, Inst Matemat, BR-21941909 Rio De Janeiro, RJ - Brazil

^[3] Univ Sao Paulo, Inst Matemat & Estat, BR-05508090 Sao Paulo, SP - Brazil

• Tipo de documento: Artigo Científico
• Fonte: DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. 40, n. 8, p. 4665-4687, AUG 2020.
• Citações Web of Science: 0

Resumo

We study the fluctuations of ergodic sums using global and local specifications on periodic points. We obtain Lindeberg-type central limit theorems in both situations. As an application, when the system possesses a unique measure of maximal entropy, we show weak convergence of ergodic sums to a mixture of normal distributions. Our results suggest decomposing the variances of ergodic sums according to global and local sources. (AU)

• Processo FAPESP: 18/15088-4 - Teoremas de limite em sistemas dinâmicos
• Beneficiário: Xuan Zhang
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado