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- W2092443373 abstract "We show that in a topological dynamical system $(X,T)$ of positive entropy there exist proper (positively) asymptotic pairs, that is, pairs $(x,y)$ such that $xnot= y$ and $lim_{nto +infty} d(T^n x,T^n y)=0$. More precisely we consider a $T$-ergodic measure $mu$ of positive entropy and prove that the set of points that belong to a proper asymptotic pair is of measure $1$. When $T$ is invertible, the stable classes (i.e., the equivalence classes for the asymptotic equivalence) are not stable under $T^{-1}$: for $mu$-almost every $x$ there are uncountably many $y$ that are asymptotic with $x$ and such that $(x,y)$ is a Li-Yorke pair with respect to $T^{-1}$. We also show that asymptotic pairs are dense in the set of topological entropy pairs." @default.
- W2092443373 created "2016-06-24" @default.
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- W2092443373 date "2019-01-02" @default.
- W2092443373 modified "2023-09-25" @default.
- W2092443373 title "Asymptotic pairs in positive-entropy systems" @default.
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