Ethan Akin and Sergii Kolyada 2003 Nonlinearity 16 1421 doi:10.1088/0951-7715/16/4/313
Li–Yorke sensitivity
Ethan Akin1 and Sergii Kolyada2
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We introduce and study a concept which links the Li–Yorke versions of chaos with the notion of sensitivity to initial conditions. We say that a dynamical system (X,T) is Li–Yorke sensitive if there exists a positive ε such that every x
X is a limit of points yX such that the pair (x,y) is proximal but not ε-asymptotic, i.e. for infinitely many positive integers i the distance ρ(Ti(x),Ti(y)) is greater than ε but for any positive δ this distance is less than δ for infinitely many i.
- PACS
- MSC
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37Axx Ergodic theory (See also 28Dxx)
37E05 Maps of the interval (piecewise continuous, continuous, smooth)
- Subjects
- Dates
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Issue 4 (July 2003)
Received 17 April 2002, in final form 8 April 2003
Published 30 May 2003
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Li–Yorke sensitivity
Ethan Akin and Sergii Kolyada 2003 Nonlinearity 16 1421
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