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There are no chaotic mappings with residual scrambled sets. (English) Zbl 0646.26008
Let f be a continuous map of a compact interval I to itself. Let $$S\subset I$$ and let for any x,y$$\in S$$, $$x\neq y$$, $$\limsup | f\quad n(x)-f\quad n(y)| >0$$ and $$\liminf | f\quad n(x)-f\quad n(y)| =0$$ for $$n\to \infty$$, where f n denotes the n-th iterate of f. Then S is residual in no subinterval of I.
Reviewer: J.Smítal

##### MSC:
 26A18 Iteration of real functions in one variable 37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior 54H20 Topological dynamics (MSC2010)
##### Keywords:
periodic point; scrambled sets; chaos
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##### References:
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