TY - JOUR
T1 - Lifting generic points
AU - Downarowicz, Tomasz
AU - Weiss, Benjamin
N1 - Publisher Copyright:
© The Author(s), 2024.
PY - 2024/9/1
Y1 - 2024/9/1
N2 - Let (X, T) and (Y, S) be two topological dynamical systems, where (X, T) has the weak specification property. Let ξ be an invariant measure on the product system (X × Y, T × S) with marginals μ on X and ν on Y, with μ ergodic. Let y ∈ Y be quasi-generic for ν. Then there exists a point x ∈ X generic for μ such that the pair (x, y) is quasi-generic for ξ. This is a generalization of a similar theorem by T. Kamae, in which (X, T) and (Y, S) are full shifts on finite alphabets.
AB - Let (X, T) and (Y, S) be two topological dynamical systems, where (X, T) has the weak specification property. Let ξ be an invariant measure on the product system (X × Y, T × S) with marginals μ on X and ν on Y, with μ ergodic. Let y ∈ Y be quasi-generic for ν. Then there exists a point x ∈ X generic for μ such that the pair (x, y) is quasi-generic for ξ. This is a generalization of a similar theorem by T. Kamae, in which (X, T) and (Y, S) are full shifts on finite alphabets.
UR - http://www.scopus.com/inward/record.url?scp=85184563996&partnerID=8YFLogxK
U2 - 10.1017/etds.2023.119
DO - 10.1017/etds.2023.119
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AN - SCOPUS:85184563996
SN - 0143-3857
VL - 44
SP - 2565
EP - 2580
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 9
ER -