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- W2078015735 abstract "Let $tau_r(x,x_0)$ be the time needed for a point $x$ to enter for the first time in a ball $B_r(x_0)$ centered in $x_0$, with small radius $r$. We construct a class of translations on the two torus having particular arithmetic properties (Liouville components with intertwined denominators of convergents) not satisfying a logarithm law, i.e. such that for generic $x,x_0$ liminf_{rto 0} frac{log tau_r(x,x_0)}{-log r} = infty. By considering a suitable reparametrization of the flow generated by a suspension of this translation, using a previous construction by Fayad, we show the existence of a mixing system on three torus having the same properties. The speed of mixing of this example must be subpolynomial, because we also show that: in a system having polynomial decay of correlations the above ratio of logarithms (which is also called the lower hitting time indicator) is bounded (it is a function of the local dimension and the speed of correlation decay). More generally, this shows that reparametrizations of torus translations having a Liouville component cannot be polynomially mixing." @default.
- W2078015735 created "2016-06-24" @default.
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- W2078015735 date "2008-01-20" @default.
- W2078015735 modified "2023-09-27" @default.
- W2078015735 title "Long hitting time, slow decay of correlations and arithmetical properties" @default.
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