We found a match
Your institution may have rights to this item. Sign in to continue.
- Title
Relative Broken Family Sensitivity.
- Authors
Liu, Zhuo Wei; Yu, Tao
- Abstract
Let π: (X, T) → (Y, S) be a factor map between two topological dynamical systems, and F a Furstenberg family of ℤ. We introduce the notion of relative broken F -sensitivity. Let F s (resp. F pubd , F inf ) be the families consisting of all syndetic subsets (resp. positive upper Banach density subsets, infinite subsets). We show that for a factor map π: (X, T) → (Y, S) between transitive systems, π is relatively broken F -sensitive for F = F s or F pubd if and only if there exists a relative sensitive pair which is an F -recurrent point of (Rπ, T(2)); is relatively broken F inf -sensitive if and only if there exists a relative sensitive pair which is not asymptotic. For a factor map π: (X, T) → (Y, S) between minimal systems, we get the structure of relative broken F -sensitivity by the factor map to its maximal equicontinuous factor.
- Subjects
DYNAMICAL systems; FAMILIES; DENSITY
- Publication
Acta Mathematica Sinica, 2024, Vol 40, Issue 9, p2297
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-024-3007-3