Furstenberg Families and Sensitivity
نویسندگان
چکیده
We introduce and study some concepts of sensitivity via Furstenberg families. A dynamical system X, f is F-sensitive if there exists a positive ε such that for every x ∈ X and every open neighborhood U of x there exists y ∈ U such that the pair x, y is not F-ε-asymptotic; that is, the time set {n : d f x , f y > ε} belongs to F, where F is a Furstenberg family. A dynamical system X, f is F1, F2 -sensitive if there is a positive ε such that every x ∈ X is a limit of points y ∈ X such that the pair x, y is F1-proximal but not F2-ε-asymptotic; that is, the time set {n : d f x , f y < δ} belongs to F1 for any positive δ but the time set {n : d f x , f y > ε} belongs to F2, where F1 and F2 are Furstenberg families.
منابع مشابه
On iteration invariants for (F1,F2)-sensitivity and weakly (F1,F2)-sensitivity of non-autonomous discrete systems
In this paper, we let (X, f1,∞) be a non-autonomous discrete system on a compact metric space X. For a positive k, the properties P̂ (k) and Q̂(k) of Furstenberg families are introduced for any integer k > 0. Based on the two properties, we prove that (F1,F2)sensitivity and weakly (F1,F2)-sensitivity are invariant under iterations. MR(2000) Subject Classification: 54H20, 54B20, 37B99, 37D45.
متن کاملIntroduction to Recurrence in Topological Dynamics: Furstenberg Families and Ellis Actions 1997 Plenum Press
متن کامل
Middle-Income Families in the Economic Downturn: Challenges and Management Strategies over Time
The “Great Recession” has hurt many families across the United States, yet most research has examined its impact on those already considered poor or working poor. However, this recession has affected middleincome families, whose experiences with economic challenge have seldom been looked at in any detail. Such families have recently been called “the new poor,” “the missing middle,” and “familie...
متن کاملOn a new schedule: transitions to adulthood and family change.
Frank Furstenberg examines how the newly extended timetable for entering adulthood is affecting, and being affected by, the institution of the Western, particularly the American, family. He reviews a growing body of research on the family life of young adults and their parents and draws out important policy implications of the new schedule for the passage to adulthood. Today, says Furstenberg, ...
متن کاملInfinite dimensional non-positively curved symmetric spaces of finite rank
This paper concerns a study of three families of non-compact type symmetric spaces of infinite dimension. Although they have infinite dimension they have finite rank. More precisely, we show they have finite telescopic dimension. We also show the existence of Furstenberg maps for some group actions on these spaces. Such maps appear as a first step toward superrigidity results.
متن کامل