On the Lebesgue Measure of Li-Yorke Pairs for Interval Maps
نویسندگان
چکیده
منابع مشابه
On the Lebesgue Measure of Li-yorke Pairs for Interval Maps
We investigate the prevalence of Li-Yorke pairs for C and C multimodal maps f with non-flat critical points. We show that every measurable scrambled set has zero Lebesgue measure and that all strongly wandering sets have zero Lebesgue measure, as does the set of pairs of asymptotic (but not asymptotically periodic) points. If f is topologically mixing and has no Cantor attractor, then typical (...
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In their celebrated ”Period three implies chaos” paper, Li and Yorke proved that if a continuous interval map f has a period 3 point then there is an uncountable scrambled set S on which f has very complicated dynamics. One question arises naturally: Can this set S be chosen invariant under f? The answer is positive for turbulent maps and negative otherwise. In this note, we shall use symbolic ...
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ژورنال
عنوان ژورنال: Communications in Mathematical Physics
سال: 2010
ISSN: 0010-3616,1432-0916
DOI: 10.1007/s00220-010-1085-9