Publication Date:
2010-01-01
Description:
We introduce and study some concepts of sensitivity via Furstenberg families. A dynamical system(X,f)isℱ-sensitive if there exists a positiveεsuch that for everyx∈Xand every open neighborhoodUofxthere existsy∈Usuch that the pair(x,y)is notℱ-ε-asymptotic; that is, the time set{n:d(fn(x),fn(y))〉ε}belongs toℱ, whereℱis a Furstenberg family. A dynamical system(X,f)is (ℱ1,ℱ2)-sensitive if there is a positiveεsuch that everyx∈Xis a limit of pointsy∈Xsuch that the pair(x,y)isℱ1-proximal but notℱ2-ε-asymptotic; that is, the time set{n:d(fn(x),fn(y))ε}belongs toℱ2, whereℱ1andℱ2are Furstenberg families.
Print ISSN:
1026-0226
Electronic ISSN:
1607-887X
Topics:
Mathematics
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